Convergence analysis of a monotone method for fourth-order semilinear elliptic boundary value problems☆

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Abstract

This work is concerned with the convergence of a monotone method for fourth-order semilinear elliptic boundary value problems. A comparison result for the rate of convergence is given. The global error is analyzed, and some sufficient conditions are formulated for guaranteeing a geometric rate of convergence.

Keywords

Fourth-order elliptic equations
Monotone method
Rate of convergence
Global error

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The work was supported in part by the National Natural Science Foundation of China No. 10001012, the Youth Science Foundation of Shanghai Higher Education No. 2000QN15, E-Institutes of Shanghai Municipal Education Commission No. E03004, Shanghai Priority Academic Discipline, and the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry.

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