Some error estimates for the lumped mass finite element method for a parabolic problem
KAUST Grant NumberKUS-C1-016-04
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AbstractWe 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.
CitationChatzipantelidis P, Lazarov RD, Thomée V (2012) Some error estimates for the lumped mass finite element method for a parabolic problem. Math Comp 81: 1–20. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02503-2.
SponsorsThe research of R.D. Lazarov was supported in parts by US NSF Grants DMS-0713829, DMS-1016525, the Pichoridis Distinguished Lectureship through the Universityof Crete in 2008, and by award KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST).
PublisherAmerican Mathematical Society (AMS)
JournalMathematics of Computation