Premium
A space‐time continuous Galerkin method with mesh modification for viscoelastic wave equations
Author(s) -
Zhao Zhihui,
Li Hong,
Luo Zhendong
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22138
Subject(s) - polygon mesh , mathematics , galerkin method , uniqueness , norm (philosophy) , discontinuous galerkin method , partial differential equation , spacetime , space time , space (punctuation) , stability (learning theory) , finite element method , wave equation , mathematical analysis , computer science , geometry , physics , quantum mechanics , chemical engineering , machine learning , political science , law , thermodynamics , engineering , operating system
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 inL ∞ ( L 2 ) 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