Two grid finite element discretization method for semi‐linear hyperbolic integro‐differential equations
In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once th...
Saved in:
| Published in | Numerical methods for partial differential equations Vol. 35; no. 5; pp. 1676 - 1693 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
01.09.2019
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0749-159X 1098-2426 |
| DOI | 10.1002/num.22370 |
Cover
| Abstract | In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once the coarse and fine mesh sizes H, h satisfy the relation h = H2 for the two‐step two grid discretization method, the two grid method achieves the same convergence accuracy as the ordinary finite element method. Both theoretical analysis and numerical experiments are given to verify the results. |
|---|---|
| AbstractList | In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once the coarse and fine mesh sizes H, h satisfy the relation h = H2 for the two‐step two grid discretization method, the two grid method achieves the same convergence accuracy as the ordinary finite element method. Both theoretical analysis and numerical experiments are given to verify the results. In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once the coarse and fine mesh sizes H , h satisfy the relation h = H 2 for the two‐step two grid discretization method, the two grid method achieves the same convergence accuracy as the ordinary finite element method. Both theoretical analysis and numerical experiments are given to verify the results. |
| Author | Chen, Yanping Chen, Luoping Huang, Yunqing |
| Author_xml | – sequence: 1 givenname: Luoping orcidid: 0000-0001-7944-500X surname: Chen fullname: Chen, Luoping organization: Southwest Jiaotong University – sequence: 2 givenname: Yanping surname: Chen fullname: Chen, Yanping email: yanpingchen@scnu.edu.cn organization: South China Normal University – sequence: 3 givenname: Yunqing surname: Huang fullname: Huang, Yunqing organization: Xiangtan University |
| BookMark | eNp9kLtOwzAUhi0EEuUy8AaWmBhCbSdO4hEhblKBpZXYItc-BkNiF9tRVSYegWfkSQgtExJMZzjf_x2dfw9tO-8AoSNKTikhbOz67pSxvCJbaESJqDNWsHIbjUhViIxy8bCL9mJ8JoRSTsUIvUyXHj8Gq7GxzibA0EIHLmFtowqQ7JtM1jvcQXryA-QDjtDZz_eP1jqQAT-tFhDmvrUKW5fgMfhhp60xEAaNlS2G137tiAdox8g2wuHP3Eezy4vp-XU2ub-6OT-bZIqJimSS11RqbWqR81JWlSRiXoDQFTOyNqoojKIauCzqWhulc13UtIS54jlQDrzM99HxxrsI_rWHmJpn3wc3nGwY4yIvakHygTrZUCr4GAOYZhFsJ8OqoaT57rIZumzWXQ7s-BerbFo_lYK07X-JpW1h9be6uZvdbhJf7EeM-A |
| CitedBy_id | crossref_primary_10_1016_j_apnum_2024_03_019 crossref_primary_10_1016_j_amc_2021_126596 crossref_primary_10_1016_j_camwa_2020_10_015 |
| Cites_doi | 10.4208/cicp.scpde14.46s 10.1137/S0036142995293493 10.1016/j.cam.2008.09.001 10.1002/nme.1775 10.1080/00207160.2017.1322689 10.1137/0732021 10.1016/0362-546X(88)90039-9 10.1002/nme.668 10.1007/BF01436618 10.1007/s10915-016-0187-8 10.1137/0728056 10.1016/j.advwatres.2011.04.010 10.1090/conm/180/01971 10.1016/j.camwa.2015.09.012 10.1137/0915016 10.1007/BF02575943 10.1016/j.cam.2016.10.030 10.1216/jiea/1181075713 10.1007/s11071-016-2843-9 10.1002/(SICI)1098-2426(199905)15:3<317::AID-NUM4>3.0.CO;2-U 10.1137/S0036142992232949 10.1090/S0025-5718-99-01180-1 10.1137/130919921 10.1080/01630569808816876 10.1007/s10915-011-9469-3 10.1216/jiea/1181075664 10.1007/BF02575729 10.1155/2012/391918 10.1016/j.cam.2009.11.043 10.1137/100810241 10.1007/BF02679436 10.1137/0727036 10.1007/BF02576527 |
| ContentType | Journal Article |
| Copyright | 2019 Wiley Periodicals, Inc. |
| Copyright_xml | – notice: 2019 Wiley Periodicals, Inc. |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D |
| DOI | 10.1002/num.22370 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Aerospace Database Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | CrossRef Aerospace Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1098-2426 |
| EndPage | 1693 |
| ExternalDocumentID | 10_1002_num_22370 NUM22370 |
| Genre | article |
| GrantInformation_xml | – fundername: Natural Science Foundation of China funderid: 91430213; 11671157; 11426189; 11501473 |
| GroupedDBID | -~X .3N .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 41~ 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABDBF ABEML ABIJN ABJNI ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACRPL ACSCC ACUHS ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFNX AFFPM AFGKR AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMVHM AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GBZZK GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ H~9 I-F IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6O MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RX1 RYL SAMSI SUPJJ TN5 UB1 V2E W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WXSBR WYISQ XBAML XG1 XPP XV2 ZZTAW ~IA ~WT AAYXX AIQQE CITATION 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c2970-a581addf89356a77a09b4e9d72fa8fc44fc1de5a488dfcd3d4816ebc53e15e563 |
| IEDL.DBID | DR2 |
| ISSN | 0749-159X |
| IngestDate | Fri Jul 25 12:17:48 EDT 2025 Wed Oct 01 04:09:16 EDT 2025 Thu Apr 24 22:56:09 EDT 2025 Wed Aug 20 07:26:47 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2970-a581addf89356a77a09b4e9d72fa8fc44fc1de5a488dfcd3d4816ebc53e15e563 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-7944-500X |
| PQID | 2259348903 |
| PQPubID | 1016406 |
| PageCount | 35 |
| ParticipantIDs | proquest_journals_2259348903 crossref_primary_10_1002_num_22370 crossref_citationtrail_10_1002_num_22370 wiley_primary_10_1002_num_22370_NUM22370 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | September 2019 2019-09-00 20190901 |
| PublicationDateYYYYMMDD | 2019-09-01 |
| PublicationDate_xml | – month: 09 year: 2019 text: September 2019 |
| PublicationDecade | 2010 |
| PublicationPlace | Hoboken, USA |
| PublicationPlace_xml | – name: Hoboken, USA – name: New York |
| PublicationTitle | Numerical methods for partial differential equations |
| PublicationYear | 2019 |
| Publisher | John Wiley & Sons, Inc Wiley Subscription Services, Inc |
| Publisher_xml | – name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc |
| References | 2001; 70 2012; 2012 2016; 19 2015; 70 1995; 32 2003; 57 2009 1988; 12 2011; 34 2014; 2014 1993; 180 1989; 26 2017; 315 1996; 33 1991; 28 1998; 19 1974; 22 1990; 27 1988; 25 1999; 15 2010; 233 1993; 30 2016; 85 1994; 16 1994; 15 2018; 95 2002; 93 2014; 52 2009; 228 2011; 49 2016; 69 2007; 69 1992; 4 1998; 35 e_1_2_8_28_1 e_1_2_8_29_1 e_1_2_8_24_1 e_1_2_8_25_1 e_1_2_8_26_1 e_1_2_8_27_1 e_1_2_8_3_1 e_1_2_8_2_1 e_1_2_8_5_1 e_1_2_8_4_1 e_1_2_8_7_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_21_1 e_1_2_8_22_1 e_1_2_8_23_1 e_1_2_8_17_1 e_1_2_8_18_1 e_1_2_8_19_1 e_1_2_8_13_1 e_1_2_8_14_1 e_1_2_8_35_1 e_1_2_8_15_1 Chen C. (e_1_2_8_36_1) 2014; 2014 e_1_2_8_16_1 e_1_2_8_37_1 Chen Y. (e_1_2_8_12_1) 1994; 16 e_1_2_8_32_1 e_1_2_8_10_1 e_1_2_8_31_1 e_1_2_8_11_1 e_1_2_8_34_1 e_1_2_8_33_1 e_1_2_8_30_1 |
| References_xml | – year: 2009 – volume: 26 start-page: 197 year: 1989 end-page: 207 article-title: Galerkin methods and error estimates for hyperbolic integro‐differential equations publication-title: Calcolo – volume: 69 start-page: 28 year: 2016 end-page: 51 article-title: error estimates of two‐grid method for miscible displacement problem publication-title: J. Sci. Comput. – volume: 4 start-page: 533 year: 1992 end-page: 584 article-title: Numerical methods for hyperbolic and parabolic integro‐differential equations publication-title: J. Integral Equations Appl. – volume: 315 start-page: 195 year: 2017 end-page: 207 article-title: A two‐level stochastic collocation method for semilinear elliptic equations with random coefficients publication-title: J. Comput. Appl. Math. – volume: 2014 start-page: 1 year: 2014 end-page: 6 article-title: A two‐grid finite element method for a second‐order nonlinear hyperbolic equation publication-title: Abstr. Appl. Anal. – volume: 15 start-page: 231 year: 1994 end-page: 237 article-title: A novel two‐grid method for semilinear equations publication-title: SIAM J. Sci. Comput. – volume: 69 start-page: 408 year: 2007 end-page: 422 article-title: Analysis of two‐grid methods for reaction‐diffusion equations by expanded mixed finite element methods publication-title: Internat. J. Numer. Methods Eng. – volume: 70 start-page: 17 year: 2001 end-page: 25 article-title: A two‐grid discretization scheme for eigenvalue problems publication-title: Math. Comp. – volume: 4 start-page: 15 year: 1992 end-page: 46 article-title: A survey of numerical methods for solving nonlinear integral equations publication-title: J. Integral Equations Appl. – volume: 25 start-page: 187 year: 1988 end-page: 201 article-title: Non‐classical H1 projection and Galerkin methods for nonlinear parabolic integro‐differential equations publication-title: Calcolo – volume: 19 start-page: 1129 year: 1998 end-page: 1153 article-title: The effect of spatial quadrature on finite element Galerkin approximations to hyperbolic integro‐differential equations publication-title: Numer. Funct. Anal. Optim. – volume: 52 start-page: 2027 year: 2014 end-page: 2047 article-title: Two‐grid methods for Maxwell eigenvalue problems publication-title: SIAM J. Numer. Anal. – volume: 70 start-page: 2474 year: 2015 end-page: 2492 article-title: A two‐grid mixed finite element method for a nonlinear fourth‐order reaction diffusion problem with time‐fractional derivative publication-title: Comput. Math. Appl. – volume: 34 start-page: 1113 year: 2011 end-page: 1123 article-title: A two‐grid method for coupled free flow with porous media flow publication-title: Adv. Water Resoure – volume: 57 start-page: 193 year: 2003 end-page: 209 article-title: A two‐grid method for expanded mixed finite‐element solution of semilinear reaction‐diffusion equations publication-title: Internat. J. Numer. Methods Eng. – volume: 15 start-page: 317 year: 1999 end-page: 332 article-title: A two‐grid method for mixed finite‐element solution of reaction‐diffusion equations publication-title: Numer. Meth. Part. D. E. – volume: 85 start-page: 2535 year: 2016 end-page: 2548 article-title: A two‐grid finite element approximation for a nonlinear time‐fractional cable equation publication-title: Nonlinear Dyn. – volume: 22 start-page: 17 year: 1974 end-page: 31 article-title: Iterative variants of the Nyström method for the numerical solution of integral equations publication-title: Numer. Math. – volume: 28 start-page: 1047 year: 1991 end-page: 1070 article-title: Ritz–Volterra projections to finite‐element spaces and applications to integrodifferential and related equations publication-title: SIAM J. Numer. Anal. – volume: 12 start-page: 785 year: 1988 end-page: 809 article-title: Finite element methods for parabolic and hyperbolic partial integro‐differential equations publication-title: Nonlinear Anal. – volume: 30 start-page: 69 year: 1993 end-page: 88 article-title: Numerical solutions for a class of differential equations in linear viscoelasticity publication-title: Calcolo – volume: 95 start-page: 1453 year: 2018 end-page: 1477 article-title: Two‐grid methods for miscible displacement problem by Galerkin methods and mixed finite‐element methods publication-title: Int. J. Comput. Math. – volume: 16 start-page: 23 year: 1994 end-page: 26 article-title: A multilevel method for finite element solutions for singular twopoint boundary value problems publication-title: Natur. Sci. J. Xiangtan Univ. – volume: 49 start-page: 383 year: 2011 end-page: 401 article-title: Two‐grid method for nonlinear reaction diffusion equations by mixed finite element methods publication-title: J. Sci. Comput. – volume: 228 start-page: 123 year: 2009 end-page: 132 article-title: Two‐grid methods for finite volume element approximations of nonlinear parabolic equations publication-title: J. Comput. Appl. Math. – volume: 2012 start-page: 255 year: 2012 end-page: 262 article-title: A two‐grid method for finite element solutions of nonlinear parabolic equations publication-title: Abstr. Appl. Anal – volume: 49 start-page: 1602 year: 2011 end-page: 1624 article-title: Two‐grid finite element discretization schemes based on shifted‐inverse power method for elliptic eigenvalue problems publication-title: SIAM J. Numer. Anal. – volume: 27 start-page: 595 year: 1990 end-page: 607 article-title: A priori error estimates for finite‐element methods for nonlinear diffusion equations with memory publication-title: SIAM J. Numer. Anal. – volume: 33 start-page: 1759 year: 1996 end-page: 1777 article-title: Two‐grid discretization techniques for linear and non‐linear PDEs publication-title: SIAM J. Numer. Anal. – volume: 93 start-page: 1 year: 2002 end-page: 51 article-title: A fast two‐grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half‐plane publication-title: Numer. Math. – volume: 180 start-page: 191 year: 1993 end-page: 203 article-title: Two‐grid method for mixed finite element approximations of non‐linear parabolic equations publication-title: Contemp. Methods – volume: 32 start-page: 501 year: 1995 end-page: 513 article-title: A fast multilevel algorithm for integral equations publication-title: SIAM J. Numer. Anal. – volume: 19 start-page: 1503 year: 2016 end-page: 1528 article-title: Two‐grid method for miscible displacement problem by mixed finite element methods and mixed finite element method of characteristics publication-title: Commun. Comput. Phys. – volume: 35 start-page: 435 year: 1998 end-page: 452 article-title: A two‐grid finite difference scheme for nonlinear parabolic equations publication-title: SIAM J. Numer. Anal. – volume: 233 start-page: 2975 year: 2010 end-page: 2984 article-title: A two‐grid method for finite volume element approximations of second‐order nonlinear hyperbolic equations publication-title: J. Comput. Appl. Math. – ident: e_1_2_8_25_1 doi: 10.4208/cicp.scpde14.46s – ident: e_1_2_8_29_1 doi: 10.1137/S0036142995293493 – ident: e_1_2_8_37_1 – ident: e_1_2_8_30_1 doi: 10.1016/j.cam.2008.09.001 – ident: e_1_2_8_16_1 doi: 10.1002/nme.1775 – ident: e_1_2_8_27_1 doi: 10.1080/00207160.2017.1322689 – ident: e_1_2_8_34_1 doi: 10.1137/0732021 – ident: e_1_2_8_5_1 doi: 10.1016/0362-546X(88)90039-9 – ident: e_1_2_8_15_1 doi: 10.1002/nme.668 – ident: e_1_2_8_32_1 doi: 10.1007/BF01436618 – ident: e_1_2_8_26_1 doi: 10.1007/s10915-016-0187-8 – ident: e_1_2_8_4_1 doi: 10.1137/0728056 – ident: e_1_2_8_28_1 doi: 10.1016/j.advwatres.2011.04.010 – ident: e_1_2_8_13_1 doi: 10.1090/conm/180/01971 – ident: e_1_2_8_23_1 doi: 10.1016/j.camwa.2015.09.012 – ident: e_1_2_8_10_1 doi: 10.1137/0915016 – ident: e_1_2_8_7_1 doi: 10.1007/BF02575943 – ident: e_1_2_8_22_1 doi: 10.1016/j.cam.2016.10.030 – volume: 2014 start-page: 1 year: 2014 ident: e_1_2_8_36_1 article-title: A two‐grid finite element method for a second‐order nonlinear hyperbolic equation publication-title: Abstr. Appl. Anal. – ident: e_1_2_8_3_1 doi: 10.1216/jiea/1181075713 – ident: e_1_2_8_24_1 doi: 10.1007/s11071-016-2843-9 – ident: e_1_2_8_14_1 doi: 10.1002/(SICI)1098-2426(199905)15:3<317::AID-NUM4>3.0.CO;2-U – ident: e_1_2_8_11_1 doi: 10.1137/S0036142992232949 – volume: 16 start-page: 23 year: 1994 ident: e_1_2_8_12_1 article-title: A multilevel method for finite element solutions for singular twopoint boundary value problems publication-title: Natur. Sci. J. Xiangtan Univ. – ident: e_1_2_8_19_1 doi: 10.1090/S0025-5718-99-01180-1 – ident: e_1_2_8_21_1 doi: 10.1137/130919921 – ident: e_1_2_8_9_1 doi: 10.1080/01630569808816876 – ident: e_1_2_8_17_1 doi: 10.1007/s10915-011-9469-3 – ident: e_1_2_8_33_1 doi: 10.1216/jiea/1181075664 – ident: e_1_2_8_2_1 doi: 10.1007/BF02575729 – ident: e_1_2_8_18_1 doi: 10.1155/2012/391918 – ident: e_1_2_8_31_1 doi: 10.1016/j.cam.2009.11.043 – ident: e_1_2_8_20_1 doi: 10.1137/100810241 – ident: e_1_2_8_35_1 doi: 10.1007/BF02679436 – ident: e_1_2_8_6_1 doi: 10.1137/0727036 – ident: e_1_2_8_8_1 doi: 10.1007/BF02576527 |
| SSID | ssj0011519 |
| Score | 2.2173336 |
| Snippet | In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1676 |
| SubjectTerms | Differential equations Discretization error estimate Finite element analysis Finite element method Grid method Linearity Mathematical analysis Nonlinear programming semi‐linear hyperbolic integro‐differential equations two‐grid discretization |
| Title | Two grid finite element discretization method for semi‐linear hyperbolic integro‐differential equations |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnum.22370 https://www.proquest.com/docview/2259348903 |
| Volume | 35 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVEBS databaseName: EBSCOhost Academic Search Ultimate customDbUrl: https://search.ebscohost.com/login.aspx?authtype=ip,shib&custid=s3936755&profile=ehost&defaultdb=asn eissn: 1098-2426 dateEnd: 20241103 omitProxy: true ssIdentifier: ssj0011519 issn: 0749-159X databaseCode: ABDBF dateStart: 20120901 isFulltext: true titleUrlDefault: https://search.ebscohost.com/direct.asp?db=asn providerName: EBSCOhost – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - HOST customDbUrl: eissn: 1098-2426 dateEnd: 20241103 omitProxy: false ssIdentifier: ssj0011519 issn: 0749-159X databaseCode: AMVHM dateStart: 20120901 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVWIB databaseName: Wiley Online Library - Core collection (SURFmarket) issn: 0749-159X databaseCode: DR2 dateStart: 19960101 customDbUrl: isFulltext: true eissn: 1098-2426 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011519 providerName: Wiley-Blackwell |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ1JS8QwFMeDzEkP7uJOEA9eOtM2O55EFBFmDuLAHITSLNXBWXQ6g-DJj-Bn9JOYNG1dUBBvhaRrkvf-r-T9HgCHDsomkJBBhqkNUBgPA8EpDZwrFpGJJeIud7jdoRddfNkjvTlwXOXCeD5E_cPNrYzCXrsFnsq89QkaOhs2rW9jLl6PEC3CqasaHWWFTlHUw3pIEViX3auoQmHcqs_86os-BOZnmVr4mfMlcFM9od9ect-cTWVTPX-DN_7zFZbBYqk_4YmfMCtgzoxWwUK7hrfma-D--mkMbyd9DbO-U6TQ-C3m0GXwuqRHn7kJffFpaFUvzM2w__by6p4oncA7G9tOpAMOQ0-jGNu2qhKLtSgDaB49YTxfB93zs-vTi6CsyRCoWLAwSAmPrEnMrMwhNGUsDYXERmgWZynPFMaZirQhqbULOlMaacwjaqQiyETEEIo2QGM0HplNAJkKEVHSmgCeYWyYoApzqozWVCHG0BY4qkYnUSWw3NXNGCQetRy7oilJ8f22wEHd9cFTOn7qtFsNcVIu1Ny2EIEwF6G7XTFWv18g6XTbxcH237vugHkrscpdabugMZ3MzJ6VMVO5X8zXd3ic8mQ |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NbtNAEF5F5QA9QKFUpKSwqjj04sT2_ktcqooo0DgHlEi5VJa9Xpcof9RJhMSJR-AZeRJmvbYJiEqIm6Vd22vPzsw3q5lvEHpjSdkUUamXUw4BipC-pyTnnnXFKjBhSqStHY5GfDChH6Zs2kJv61oYxw_RHLhZzSjttVVweyDd22MN3S274NwEBOwPKIc4xUKijw15FECdsq0H-EjlgdOe1rxCfthrbv3dG_2CmPtAtfQ0_Sfopl6jSzCZd3fbtKu__kHf-L8fcYQeVxAUX7o98xS1zOoZOowa_tbNMZqPv6zxbTHLcD6zoBQbl2WObRGvrXt0xZvY9Z_GAHzxxixnP759t0tKCvwJwtsitZzD2BFSrGGsbsYCRmWBzZ0jGd88R5P-u_HVwKvaMng6VML3EiYDsIo5IB3GEyESX6XUqEyEeSJzTWmug8ywBExDluuMZFQG3KSaERMwwzg5QQer9cq8QFhonzCdghWQOaVGKK6p5NpkGddECNJGF7V4Yl1xltvWGYvYsS2Htm9KXP6_Njpvpn52RB1_m9SpZRxXurqBEaYIlcq3ryuFdf8D4tEkKi9O_33qa_RwMI6G8fD96PolegSIq0pS66CDbbEzZ4BqtumrcvP-BJiD9oU |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ1bS9xAFMcHsSD1wda24lprh9KHvmRNMnfwRdRF2-5Sigv7UkIyF13UXd0LBZ_8CH5GP4lnMklqSwXxLTCT68yc859wzu8g9NlD2RRRReQohw2KkHGkJOeRd8UqsWlBpM8d7vb4YZ9-HbDBAtqpc2ECH6L54eZXRmmv_QK3l8ZtP6CGzi_a4NwEbNhfUKakD-jb_9nAo0DqlGU9wEeqCJz2oOYKxel2c-rf3uiPxHwoVEtP03mFftXPGAJMztrzWdHW1__gG5_7Eq_RSiVB8W6YM6towY7eoOVuw2-dvkVnx7_H-GQyNNgNvSjFNkSZY5_E6_MeQ_ImDvWnMQhfPLUXw7ubW_9I-QSfwvZ2UnjmMA5AijG01cVYwKicY3sVIOPTd6jfOTjeO4yqsgyRTpWIo5zJBKyiA6XDeC5EHquCWmVE6nLpNKVOJ8ayHEyDcdoQQ2XCbaEZsQmzjJM1tDgaj-w6wkLHhOkCrIB0lFqhuKaSa2sM10QI0kJf6uHJdMUs96UzzrNAW0593ZSs_H4t9KnpehlAHf_rtFmPcVat1Sm0MEWoVLG_XTlYj18g6_W75cHG07t-REs_9jvZ96Pet_foJQiuKkZtEy3OJnP7AUTNrNgq5-49Tu_2CQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Two+grid+finite+element+discretization+method+for+semi%E2%80%90linear+hyperbolic+integro%E2%80%90differential+equations&rft.jtitle=Numerical+methods+for+partial+differential+equations&rft.au=Chen%2C+Luoping&rft.au=Chen%2C+Yanping&rft.au=Huang%2C+Yunqing&rft.date=2019-09-01&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=0749-159X&rft.eissn=1098-2426&rft.volume=35&rft.issue=5&rft.spage=1676&rft.epage=1693&rft_id=info:doi/10.1002%2Fnum.22370&rft.externalDBID=10.1002%252Fnum.22370&rft.externalDocID=NUM22370 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0749-159X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0749-159X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0749-159X&client=summon |