A two-grid algorithm for expanded mixed finite element approximations of semi-linear elliptic equations

Authors:
Wei Liu;Hongxing Rui;Fengzhu Hu
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 8
Cited 0

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Abstract

A semi-linear elliptic problem with variable coefficient is approximated by expanded mixed formulation based on the RTN and BDM mixed finite elements. In order to solve the nonlinear approximation system of equations efficiently, a two-grid algorithm is considered and discussed in this paper. The work includes a small nonlinear system on a coarse grid space with mesh size H and a linear system on a fine grid space with mesh size h. It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H=O(h^1^/^2) in the L^2 norm. Some numerical examples are presented to illustrate the theoretical results.