Dirichlet Boundary Value Correction using Lagrange Multipliers
It addresses the problem of enforcing Dirichlet boundary conditions on curved boundaries in finite element methods, offering a correction that maintains accuracy.
The paper proposes a boundary value correction method for curved boundaries approximated by straight lines using Lagrange multipliers, achieving optimal convergence for polynomial orders up to 3.
We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to the Taylor series expansion approach used by Bramble, Dupont and Tomée [Math. Comp., 26:869--879, 1972] in the context of Nitsche's method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.