Finite element method application of ERBS triangles

Abstract

In this paper we solve an eigenvalue problem on a circular membrane with fixed outer boundary by using a finite element method, where an element is represented as an expo-rational blending triangle. ERBS triangles combine properties of B-spline finite elements and standard polynomial triangular elements. The overlapping of local triangles allows us to provide a flexible handling of the surface while preserving the smoothness of the initial domain, also over the nodes and edges. Blending splines accurately approximate the outer boundary, while keeping a coarse discretization of the domain. We consider a mesh construction for such type of elements, evaluating of basis functions and their directional derivatives, local-to-global mapping, assembling of element matrices.