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A priori error analysis of the mortar finite element method for variational inequalities
Article first published online: 19 JUN 2007
DOI: 10.1002/num.20279
Copyright © 2007 Wiley Periodicals, Inc.
Issue
1098-2426/asset/cover.gif?v=1&s=154034efe243561f5d5a1ba4ea980eecb3daee40 "Numerical Methods for Partial Differential Equations")
Numerical Methods for Partial Differential Equations
Volume 24, Issue 2, pages 476–503, March 2008
Additional Information
How to Cite
Jiang, B. (2008), A priori error analysis of the mortar finite element method for variational inequalities. Numerical Methods for Partial Differential Equations, 24: 476–503. doi: 10.1002/num.20279
Publication History
- Issue published online: 28 JAN 2008
- Article first published online: 19 JUN 2007
- Manuscript Accepted: 10 APR 2007
- Manuscript Received: 26 JUL 2006
- Abstract
- References
- Cited By
Keywords:
- mortar finite element method;
- domain decomposition;
- variational inequality;
- free seepage flow;
- obstacle problem
Abstract
The mortar finite element method is a special domain decomposition method, which can handle the situation where meshes on different subdomains need not align across the interface. In this article, we will apply the mortar element method to general variational inequalities of free boundary type, such as free seepage flow, which may show different behaviors in different regions. We prove that if the solution of the original variational inequality belongs to H2(D), then the mortar element solution can achieve the same order error estimate as the conforming P1 finite element solution. Application of the mortar element method to a free surface seepage problem and an obstacle problem verifies not only its convergence property but also its great computational efficiency. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008