Mesh grading technique using modified isoparametric shape functions and its application to wave propagation problems

Mesh grading of finite element meshes is greatly simplified by allowing two or more finer elements to abut the entire straight or curved edge of a neighbouring coarser element. This paper proposes the technique by which it can be achieved while maintaining inter‐element compatibility by introducing modified shape functions. The concepts and potential advantages of this technique are described in detail for two‐dimensional isoparametric quadrilateral elements, although the same procedure can also be applied to other element types including three‐dimensional. Implementation of this technique to existing finite element programs requires only minimal modifications. Finally, numerical examples are presented to illustrate the application of the mesh grading technique to several wave propagation problems.