Multilevel correction adaptive finite element method for semilinear elliptic equation

Applications of mathematics

关键词: semilinear elliptic problem;    multilevel correction;    adaptive finite element method;   

DOI  :  

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation 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, solving the semilinear elliptic problem can reach almost the same efficiency 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.

【 授权许可】

Unknown