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A Lumped Mass Finite-element Method with Quadrature for a Non-linear Parabolic Problem

Authors:	NIE YI-YONG; THOMEE VIDAR

Institution:	Shenyang Institute of Computing Technology, Academia Simica Shenyang, Peoples Republic of China Department of Mathematics, Chalmers University of Technology and The University of G $o$ teborg S-412 96 Göteborg, Sweden

Abstract:	For a non-linear second-order parabolic equation in two spacedimensions we consider semidiscrete and totally discrete variantsof the lumped mass modification with quadrature of the standardGalerkin method using piecewise linear approximating functions.We demonstrate error estimates of optimal order in L₂ and ofalmost optimal order in L and discuss some positivity and monotonicityproperties of the discrete solution operator.

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