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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2014

01.05.2014

A \(C^0\)-Weak Galerkin Finite Element Method for the Biharmonic Equation

verfasst von: Lin Mu, Junping Wang, Xiu Ye, Shangyou Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2014

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Abstract

A \(C^0\)-weak Galerkin (WG) method is introduced and analyzed in this article for solving the biharmonic equation in 2D and 3D. A discrete weak Laplacian is defined for \(C^0\) functions, which is then used to design the weak Galerkin finite element scheme. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established for the weak Galerkin finite element solution in both a discrete \(H^2\) norm and the standard \(H^1\) and \(L^2\) norms with appropriate regularity assumptions. Numerical results are presented to confirm the theory. As a technical tool, a refined Scott-Zhang interpolation operator is constructed to assist the corresponding error estimates. This refined interpolation preserves the volume mass of order \((k+1-d)\) and the surface mass of order \((k+2-d)\) for the \(P_{k+2}\) finite element functions in \(d\)-dimensional space.
Vorheriger Artikel Composite Spectral Method for Exterior Problems with Polygonal Obstacles
Nächster Artikel A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

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Metadaten
Titel
A -Weak Galerkin Finite Element Method for the Biharmonic Equation
verfasst von
Lin Mu
Junping Wang
Xiu Ye
Shangyou Zhang
Publikationsdatum
01.05.2014
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-013-9770-4

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