The effective interface approach for coupling of the FE and meshless FD methods and applying essential boundary conditions

The paper presents a new effective technique for coupling two computational methods with different types of discretization and approximation. It is based on a concept of two adjacent subdomains which are connected with each other by means of a thin layer of material. Each of the subdomain may have a different discretization structure and approximation base. The standard Finite Element Method (FEM) as well as the meshless Finite Difference Method (MFDM) are applied here to be coupled. However, the coupling can be used for any other methods. The same concept is used for applying the essential boundary conditions for both of the methods. The width of the interface layer, depending on discretization density, is evaluated by means of several heuristic assumptions. The paper is illustrated with selected two- and three-dimensional examples.