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Singular function mortar finite element methods
Sarkis, Marcus Tu, Xuemin
Sarkis, Marcus
Tu, Xuemin
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Abstract
We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular functions. The main idea introduced in this paper is the replacement of cut-off functions by mortar element techniques on the boundary of the domain. As advantages, the new discretizations do not require costly numerical integrations and have smaller a priori error estimates and condition numbers. Based on such an approach, we prove optimal accuracy error bounds for the discrete solution. Based on such techniques, we also derive new extraction formulas for the stress intensive factor. We establish optimal accuracy for the computed stress intensive factor. Numerical examples are presented to support our theory.
Description
This is the published version, also available here: http://dx.doi.org/10.2478/cmam-2003-0014.
Date
2003-01-05
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De Gruyter Open
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Keywords
mortar discretization, corner singularity, nonconforming finite element
Citation
Sarkis, Marcus & Tu, Xuemin. "Singular function mortar finite element methods." Computational Methods in Applied Mathematics Comput. Methods Appl. Math.. Volume 3, Issue 1, Pages 202–218. (2003) http://dx.doi.org/10.2478/cmam-2003-0014.