Multilevel Correction Adaptive Finite Element Method For Semilinear Elliptic Equation

*Qichen Hong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences) hongqichen@lsec.cc.ac.cn

A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. In our scheme, the semilinear elliptic problem is transformed into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence the efficiency of solving the semilinear elliptic problem can reach almost the same as the adaptive method for the associated boundary value problem. The convergence and optimal complexity of the new scheme can be derived theoretically and demonstrated numerically.