The finite element method with Lagrange multipliers for domains with corners

Author:
Juhani Pitkäranta

Journal:
Math. Comp. **37** (1981), 13-30

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616357-9

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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DOI:
https://doi.org/10.1090/S0025-5718-1981-0616357-9

Article copyright:
© Copyright 1981
American Mathematical Society