A space‐time continuous Galerkin method with mesh modification for viscoelastic wave equations |
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| Authors: | Zhihui Zhao Hong Li Zhendong Luo |
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| Affiliation: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, China;2. School of Mathematics and Physics, North China Electric Power University, Beijing, China |
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| Abstract: | In this article, we consider the space‐time continuous Galerkin (STCG) method for the viscoelastic wave equations. It allows variable temporal step‐sizes, and the changing of the spatial grids in two adjacent time levels. The existence, uniqueness, and stability of the approximate solutions are demonstrated and the error estimates with global and local spatial mesh sizes in  norm are derived without any restrictive assumptions on the space‐time meshes. If the meshes in each time level satisfy some reasonable assumptions, then we can get the optimal order error estimates both in time and space. Finally, we give a numerical example on unstructured meshes to confirm the theoretical findings. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1183–1207, 2017 |
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| Keywords: | numerical example optimal order error estimates space‐time continuous Galerkin method viscoelastic wave equations |
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norm are derived without any restrictive assumptions on the space‐time meshes. If the meshes in each time level satisfy some reasonable assumptions, then we can get the optimal order error estimates both in time and space. Finally, we give a numerical example on unstructured meshes to confirm the theoretical findings. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1183–1207, 2017