A non-conforming finite element method for sub-meshing.
The authors study non-conforming finite elements in the discretization of the Laplacian, where the solution domain is subdivided by regions with different degrees of refinement. The use of non-conforming elements is of special interest when the different levels of refinement do not match across the boundaries of the subdivision. The authors analyse a model problem consisting of the Laplacian in a domain formed by the union of two rectangles with mixed Dirichlet and Neumann boundary conditions. For the transition between the two subdomains interface elements are used. The main result of the paper is a bound for the error in the energy norm by the sum of the approximation and the consistency error. Some numerical results are presented for both the \(h\)- and the \(p\)-version of finite elements.
mixed Dirichlet and Neumann boundary conditions
scientific article; zbMATH DE number 1978028