Lumped Mass Metheds For Parabolic Type Equations

In this paper, we consider lumped mass metheds for parabolic type integro-differential equations.In chapter one,we consider A Lumped Mass Finite Element Method for the linear integro-differential equationj, and nonlinear integro-differential equationin two dimensions. For the linear integro-differential equation we obtain W1'11-optimal and Lp-optimal estimates and superconvergence estimate of U ?V^u; for the nonlinear equation we obtain W1}P and I/2-optimal estimates only.In chapter two,we consider a lumped mass generalized difference scheme for linear integro-differential equation in two dimensions.Lp and error estimates of the generalized Ritz-Volterra projection u ?V and and -norm error estimates of Dk = 1,2 are made,then we obtain and -norm error estimates of u?...