Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data Academic Article uri icon

abstract

  • 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.

author list (cited authors)

  • Sinha, R. K., Ewing, R. E., & Lazarov, R. D.

citation count

  • 21

publication date

  • January 2009