The finite element method with Lagrange multipliers for domains with corners
Juhani Pitkäranta · Mathematics of Computation · 1981
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.