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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The finite element method with Lagrange multipliers for domains with corners

Author: Juhani Pitkäranta
Journal: Math. Comp. 37 (1981), 13-30
MSC: Primary 65N30
MathSciNet review: 616357
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Abstract: We study the convergence of the finite element method with Lagrange multipliers for approximately solving the Dirichlet problem for a second-order elliptic equation in a plane domain with piecewise smooth boundary. Assuming mesh refinements around the corners, we construct families of boundary subspaces that are compatible with triangular Lagrange elements in the interior, and we carry out the error analysis of the resulting approximations in weighted Sobolev spaces.

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Article copyright: © Copyright 1981 American Mathematical Society