A two-gird method for finite element solution of parabolic integro-differential equations

Analysis of Two-Grid Characteristic Finite Element Methods for Convection-Diffusion Equations

“…As we know, the two-grid method is a highly efcient and accurate method, which was frst formulated for nonsymmetric linear and nonlinear elliptic problems by Xu [17,18]. Due to the better practical performance, the twogrid method was applied and investigated for other types of problems by many authors (see [12,[19][20][21][22][23][24][25]). Among them, Bi and Ginting [19] have given the two-grid discontinuous Galerkin method for a quasi-linear elliptic problem, Li and Tan [20] have used the two-grid method for nonlinear hyperbolic equations, Dawson and Wheeler [21] have used two-grid mixed fnite element methods for nonlinear parabolic equations, and Chen et al [22,23] have considered the two-grid method for nonlinear reaction-difusion equations by the expanded mixed fnite element method.…”

“…In particular, Qin and Ma [12] have constructed and analysed a two-step algorithm by using a two-grid idea for the characteristic fnite element solution of nonlinear convection-difusion equations. Recently, we have proposed the two-grid algorithms based on the mixed fnite element approximation for nonlinear hyperbolic equations [24] and studied the unconditional error estimates of two-gird fnite element methods for parabolic integrodiferential equations [25]. In the abovementioned works, the theoretical study and numerical experiments show that the two-grid technique is computationally more efcient than the original method.…”