SOME ERROR ESTIMATES FOR THE LUMPED MASS FINITE ELEMENT METHOD FOR A PARABOLIC PROBLEM Academic Article

abstract

• 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.

authors

• Lazarov, Raytcho

published proceedings

• MATHEMATICS OF COMPUTATION

author list (cited authors)

• Chatzipantelidis, P., Lazarov, R. D., & Thomee, V.

citation count

• 15

publication date

• January 2012

publisher

• American Mathematical Society (AMS)  Publisher

keywords

• Error Estimates
• Lumped Mass Method
• Nonsmooth Initial Data
• Parabolic Partial Differential Equations

Digital Object Identifier (DOI)

• 10.1090/s0025-5718-2011-02503-2

start page

• 1

end page

• 20

volume

• 81

issue

• 277

URL

• http://dx.doi.org/10.1090/s0025-5718-2011-02503-2