Approximate and Low Regularity Dirichlet Boundary Conditions in the Generalized Finite Element Method

摘要

We propose a method for treating the Dirichlet boundary conditions in the framework of the Generalized Finite Element Method (GFEM). We are especially interested in boundary data with low regularity (possibly a distribution). We use approximate Dirichlet boundary conditions as in 11 and polynomial approximations of the boundary. Our sequence of GFEMspaces considered, S , = 1, 2, . . . is such that S not subset H1(sub 0) (omega), and hence it does not conform to one of the basic FEM conditions. Let h be the typical size of the elements defining S and let epilson H(exp)(m+1)(omega) be the solution of the Poisson problem Deltau = f in omega, u = 0 on derivative omega, on a smooth, bounded domain omega.