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Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
Author(s) -
Chatzipantelidis P.,
Lazarov R. D.,
Thomée V.
Publication year - 2004
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.20006
Subject(s) - mathematics , finite element method , backward euler method , projection (relational algebra) , piecewise , mathematical analysis , finite volume method , effective domain , piecewise linear function , rate of convergence , mixed finite element method , bilinear interpolation , regular polygon , norm (philosophy) , domain (mathematical analysis) , euler equations , geometry , convex analysis , convex optimization , algorithm , channel (broadcasting) , statistics , physics , political science , mechanics , law , electrical engineering , thermodynamics , engineering
Abstract We analyze the spatially semidiscrete piecewise linear finite volume element method for parabolic equations in a convex polygonal domain in the plane. Our approach is based on the properties of the standard finite element Ritz projection and also of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite volume element method. Because the domain is polygonal, special attention has to be paid to the limited regularity of the exact solution. We give sufficient conditions in terms of data that yield optimal order error estimates in L 2 and H 1. The convergence rate in the L ∞ norm is suboptimal, the same as in the corresponding finite element method, and almost optimal away from the corners. We also briefly consider the lumped mass modification and the backward Euler fully discrete method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004