Year: 2023
Author: Xiu Ye, Shangyou Zhang
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 855–869
Abstract
A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at the same time. The ultra simple formulation of the method will reduce programming complexity in practice. Optimal order error estimates in a discrete $H^2$ norm is established for the corresponding finite element solutions. Error estimates in the $L^2$ norm are also derived with a sub-optimal order of convergence for the lowest order element and an optimal order of convergence for all high order of elements. Numerical results are presented to confirm the theory of convergence.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1037
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 855–869
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: finite element methods weak Laplacian biharmonic equations polyhedral meshes.
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