Error estimates of the lumped mass finite element method for semilinear elliptic problems

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摘要

We are concerned with the semilinear elliptic problems. We first investigate the L2-error estimate for the lumped mass finite element method. We then use the cascadic multigrid method to solve the corresponding discrete problem. On the basis of the finite element error estimates, we prove the optimality of the proposed multigrid method. We also report some numerical results to support the theory.

论文关键词:65N12,65N30,65N55,Semilinear elliptic problem,Lumped mass discretization,L2-error estimate,Cascadic multigrid method

论文评审过程:Received 11 December 2010, Revised 27 October 2011, Available online 19 November 2011.

论文官网地址:https://doi.org/10.1016/j.cam.2011.11.009