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Developing weak Galerkin finite element methods for the wave equation
Author(s) -
Huang Yunqing,
Li Jichun,
Li Dan
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.22127
Subject(s) - galerkin method , mathematics , discontinuous galerkin method , partial differential equation , finite element method , convergence (economics) , mathematical analysis , wave equation , hyperbolic partial differential equation , stability (learning theory) , elliptic partial differential equation , physics , computer science , machine learning , economics , thermodynamics , economic growth
In this article, we extend the recently developed weak Galerkin method to solve the second‐order hyperbolic wave equation. Many nice features of the weak Galerkin method have been demonstrated for elliptic, parabolic, and a few other model problems. This is the initial exploration of the weak Galerkin method for solving the wave equation. Here we successfully developed and established the stability and convergence analysis for the weak Galerkin method for solving the wave equation. Numerical experiments further support the theoretical analysis. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 868–884, 2017