Geodesic
Multilevel correction adaptive finite element method for semilinear elliptic equation
Applications of Mathematics, Tome 60 (2015) no. 5, pp. 527-550.

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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.
DOI : 10.1007/s10492-015-0110-x
Classification : 35J61, 62F35, 65B99, 65N30
Keywords: semilinear elliptic problem; multilevel correction; adaptive finite element method 
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     title = {Multilevel correction adaptive finite element method for semilinear elliptic equation},
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Lin, Qun; Xie, Hehu; Xu, Fei. Multilevel correction adaptive finite element method for semilinear elliptic equation. Applications of Mathematics, Tome 60 (2015) no. 5, pp. 527-550. doi : 10.1007/s10492-015-0110-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0110-x/

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