Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping |
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Authors: | Liyong Zhu Qiang Du |
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Affiliation: | a LMIB and School of Mathematics and System Science, Beihang University, 100191, Beijing, PR Chinab Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA |
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Abstract: | In this paper, based on some mesh-dependent estimates on the extreme eigenvalues of a general finite element system defined on a simplicial mesh, novel and sharp bounds on the permissible time step size are derived for the mass lumping finite element approximations of parabolic equations. The bounds are dependent not only on the mesh size but also on the mesh shape. These results provide guidance to the stability of numerical solutions of parabolic problems in relation to the unstructured geometric meshing. Numerical experiments on both uniform meshes and adaptive meshes are presented to validate the theoretical analysis. |
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Keywords: | Stable time step size Finite element method Unstructured mesh Parabolic equation Mass lumping |
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