MIXED FINITE ELEMENT APPROXIMATIONS OF PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH INITIAL DATA
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We analyze the semidiscrete mixed .nite element methods for parabolic integrodi .erential equations that arise in the modeling of nonlocal reactive .ows in porous media. A priori L2-error estimates for pressure and velocity are obtained with both smooth and nonsmooth initial data. More precisely, a mixed Ritz-Volterra projection, introduced earlier by Ewing et al. in [SIAM J. Numer. Anal., 40 (2002), pp. 1538-1560], is used to derive optimal L2-error estimates for problems with initial data in H2 H1 0 . In addition, for homogeneous equations we derive optimal L2-errorestimates for initial data just in L2. Here, we use an elementary energy technique and duality argument. 2009 Society for Industrial and Applied Physics.
SIAM JOURNAL ON NUMERICAL ANALYSIS
author list (cited authors)
Sinha, R. K., Ewing, R. E., & Lazarov, R. D.
complete list of authors
Sinha, Rajen K||Ewing, Richard E||Lazarov, Raytcho D