OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

DEEPJYOTI GOSWAMI, AMIYA K. PANI, SANGITA YADAV

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    3 Scopus citations

    Abstract

    AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.
    Original languageEnglish (US)
    Pages (from-to)245-266
    Number of pages22
    JournalThe ANZIAM Journal
    Volume55
    Issue number3
    DOIs
    StatePublished - Jun 5 2014

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