A cascadic multigrid method for a kind of semilinear elliptic problem

Abstract

In this paper, we analyze a cascadic multigrid method for semilinear elliptic problems in which the derivative of the semilinear term is Holder continuous. We first investigate the standard finite element error estimates of this kind of problem. We then solve the corresponding discrete problems using the cascadic multigrid method. We prove that the algorithm has an optimal order of convergence in energy norm and quasi-optimal computational complexity. We also report some numerical results to support the theory.