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$H^1$-Galerkin mixed finite element methods for parabolic partial integro-differential equations. (English) Zbl 1008.65101
$H^1$-Galerkin mixed element methods are studied for the numerical solution of parabolic partial integro-differential equations which arise in mathematical models of reactive flows in porous media and of materials with memory effects. Optimal error estimates are derived for semidiscrete and fully discrete schemes for problems in one space dimension. The extension to problems in two and three space variables is also discussed. The $H^1$-Galerkin mixed finite element approximations have the same rate of convergence as the classical methods without requiring the LBB consistency condition.

65R20Integral equations (numerical methods)
45K05Integro-partial differential equations
76S05Flows in porous media; filtration; seepage
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