半线性椭圆问题的自适应有限元分析

Adaptive finite element analysis for semilinear elliptic problems

本文既不利用非线性问题的单调性,也不利用有限元逼近的一致有界性进行半线性椭圆问题的自适应有限元分析.本文先推导有限元逼近解的先验和后验误差估计,然后,利用这些估计,分析一类自适应有限元算法,特别是,得到该算法的收敛率和复杂度.

In this paper, without using the uniform boundedness of finite element approximations, we derive both a priori and a posteriori finite element error estimates for a class of semilinear elliptic problems, based on which we analyze an adaptive finite element method to approximate the solutions of this kind of semilinear problems. In particular, we obtain the convergence rate and complexity of the adaptive finite element method.