A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron

A -conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomial...

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Bibliographic Details
Published inJournal of numerical mathematics Vol. 30; no. 3; pp. 163 - 172
Main Authors Ye, Xiu, Zhang, Shangyou
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.09.2022
Walter de Gruyter GmbH
Subjects
65N15
65N30
biharmonic equation
Biharmonic equations
finite element
Finite element method
Polynomials
Tetrahedra
Triangles
triangular mesh
weak gradient
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ISSN1570-2820
1569-3953
DOI10.1515/jnma-2021-0012

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Summary:A -conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non ) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete -norm and the -norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.
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ISSN:1570-2820
1569-3953
DOI:10.1515/jnma-2021-0012