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A priori error analysis of the mortar finite element method for variational inequalities
Author(s) -
Jiang Bin
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20279
Subject(s) - mortar methods , obstacle problem , domain decomposition methods , finite element method , variational inequality , mathematics , mortar , polygon mesh , convergence (economics) , a priori and a posteriori , domain (mathematical analysis) , boundary (topology) , boundary value problem , mathematical analysis , mixed finite element method , extended finite element method , geometry , structural engineering , engineering , philosophy , archaeology , epistemology , economics , history , economic growth
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 H 2 ( D ), then the mortar element solution can achieve the same order error estimate as the conforming P 1 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