Mathematica implementation of the high order finite element method applied to eigenproblems

In this paper an hp-FEM implementation on Mathematica is discussed. FEM-implementations on higher-level programming platforms are useful for prototyping new algorithms and ideas, but also serve as testing ground for interesting programming techniques. Here, an hp-adaptive algorithm for eigenproblems, and the use of precomputed data and generation of highly graded hp-meshes, are examples of the former and latter, respectively. The performance of the code is evaluated in relation to a suite of benchmark problems for the Laplacian and thin solids in elasticity.