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A posteriori error estimates for finite element approximations to the wave equation with discontinuous coefficients
Author(s) -
Deka Bhupen
Publication year - 2019
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.22368
Subject(s) - mathematics , a priori and a posteriori , norm (philosophy) , finite element method , residual , interpolation (computer graphics) , convergence (economics) , wave equation , a priori estimate , mathematical analysis , mathematical optimization , algorithm , animation , philosophy , physics , computer graphics (images) , epistemology , political science , computer science , law , economics , thermodynamics , economic growth
We derive residual‐based a posteriori error estimates of finite element method for linear wave equation with discontinuous coefficients in a two‐dimensional convex polygonal domain. A posteriori error estimates for both the space‐discrete case and for implicit fully discrete scheme are discussed in L ∞ ( L 2 ) norm. The main ingredients used in deriving a posteriori estimates are new Clément type interpolation estimates in conjunction with appropriate adaption of the elliptic reconstruction technique of continuous and discrete solutions. We use only an energy argument to establish a posteriori error estimates with optimal order convergence in the L ∞ ( L 2 ) norm.