A localized orthogonal decomposition method for semi-linear elliptic problems
Journal article, 2014

In this paper we propose and analyze a localized orthogonal decomposition (LOD) method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. This Galerkin-type method is based on a generalized finite element basis that spans a low dimensional multiscale space. The basis is assembled by performing localized linear fine-scale computations on small patches that have a diameter of order H | log (H) | where H is the coarse mesh size. Without any assumptions on the type of the oscillations in the coefficients, we give a rigorous proof for a linear convergence of the H1-error with respect to the coarse mesh size even for rough coefficients. To solve the corresponding system of algebraic equations, we propose an algorithm that is based on a damped Newton scheme in the multiscale space.

Author

P. Henning

Axel Målqvist

Daniel Peterseim

Mathematical Modelling and Numerical Analysis

28227840 (ISSN) 28047214 (eISSN)

Vol. 48 5 1331-1349

Subject Categories

Computational Mathematics

DOI

10.1051/m2an/2013141

More information

Created

10/10/2017