The Concept of Dividing Lines/Surfaces for the Finite Difference Element Method (FDEM)

The FDEM (Finite Difference Element Method) is a black‐box solver for the solution of nonlinear systems of elliptic and parabolic PDEs 1]. We use a FDM of arbitrary consistency order on an unstructured FEM mesh. We compute a reliable error estimate which we also use for an automatic consistency order control and mesh refinement. By dividing lines (2‐D) or dividing surfaces (3‐D) we extend this method for the uniform solution over coupled domains.