Some error estimates for the lumped mass finite element method for a parabolic problem

P. Chatzipantelidis, R. D. Lazarov, V. Thomée

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We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation. We also discuss the application to time discretization by the backward Euler and Crank-Nicolson methods. © 2011 American Mathematical Society.
Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalMathematics of Computation
Issue number277
StatePublished - Jan 1 2012
Externally publishedYes

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