The hierarchically graded multilevel finite element method

Abstract

 Using higher p-order ansatz functions in the finite element method achieves already with a rather small number of elements good approximations of the smooth part of the solution. For covering this part the p-method is more efficient than the h-method. Otherwise is a high p-order too expensive according to computational effort to use it on a large number of elements which might be necessary to approximate the solution in disturbed areas of a structure. We present an ansatz space which balances the good approximation quality of higher p-ansatz with their computational cost by assigning each level of an hierarchical sequence of meshes an own adequate ansatz space.