Premium
Difference approximations for wave equations via finite elements II. Error analysis
Author(s) -
Card Curtis L.,
Allen Myron B.
Publication year - 1995
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.1690110204
Subject(s) - quadrature (astronomy) , finite element method , mathematics , grid , discontinuous galerkin method , galerkin method , approximations of π , wave equation , finite difference , stiffness , finite difference method , mathematical analysis , geometry , physics , optics , thermodynamics
Difference‐like schemes for the wave equation arise naturally from a Galerkin finite‐element formulation, if we adopt certain quadrature rules in evaluating the mass and stiffness matrices. One can extend these schemes to problems involving sharp interfaces by applying the quadrature on a refinement of the finite‐element grid that includes the interfaces. We develop error estimates for this modified scheme that corroborate numerical results for acoustic and elastic wave equations, presented in a companion article. © 1995 John Wiley & Sons, Inc.