Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-local Boundary Conditions

We present an efficient Legendre–Galerkin method and its error analysis for a class of PDEs with non-local boundary conditions. We also present several numerical experiments, including the scattering problem from an open cavity, to demonstrate the accuracy and efficiency of the proposed method.

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Bibliographic Details
Published inJournal of scientific computing Vol. 68; no. 2; pp. 417 - 437
Main Authors Hu, Lina, Ma, Lina, Shen, Jie
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2016
Springer Nature B.V
Subjects
Algorithms
Approximation
Boundary conditions
Computational Mathematics and Numerical Analysis
Elliptic differential equations
Error analysis
Estimates
Fourier transforms
Galerkin method
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Partial differential equations
Theoretical
Error analysis
65N35
Spectral-Galerkin method
Non-local boundary conditions
35J05
35J25
65N22
Legendre polynomial
65F05
Online AccessGet full text
ISSN0885-7474
1573-7691
DOI10.1007/s10915-015-0145-x

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Summary:We present an efficient Legendre–Galerkin method and its error analysis for a class of PDEs with non-local boundary conditions. We also present several numerical experiments, including the scattering problem from an open cavity, to demonstrate the accuracy and efficiency of the proposed method.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-015-0145-x