A full discrete two-grid finite-volume method for a nonlinear parabolic problem

Abstract

A fully discrete two-grid finite-volume method (FVM) for a nonlinear parabolic problem is studied in this paper. This method involves solving a nonlinear parabolic equation on coarse mesh space and a linearized parabolic equation on fine grid. Both L 2 and H 1 norm error estimates of the standard FVM for the nonlinear parabolic problem are derived. Compared with the standard FVM, the two-level method is of the same order as the one-level method in the H 1-norm as long as the mesh sizes satisfy h=𝒪(H 3/2). However, the two-level method involves much less work than the standard method. Numerical results are provided to demonstrate the effectiveness of our algorithm.