We consider fourth order singularly perturbed boundary value problems (BVPs) in one-dimension and the approximation of their solution by the hp version of the Finite Element Method (FEM). If the given problem’s boundary conditions are suitable for writing the BVP as a second order system, then we construct an hp FEM on the so-called Spectral Boundary Layer Mesh that gives a robust approximation...

We study the approximation of the Reissner-Mindlin plate using the p/hp version of the finite element method (FEM). Our goal is to identify a method that: (i) is free of shear locking, (ii) approximates the boundary layer independently of the thickness of the plate and (iii) converges exponentially with respect to the number of degrees of freedom. We will consider both standard and reduced cons...

An algorithm for non-intrusively coupling a commercial finite element software with a research code implementing a hierarchical enrichment of finite element spaces is presented. Examples of hierarchical methods supported by the algorithm are the Generalized or eXtended FEM (GFEM), the scale-bridging GFEM with numerically defined enrichment functions (GFEMgl), and the p-version of the FEM. The p...

Absac The h-p-version of finite-elements delivers a sub-exponential conver gence in the energy norm. A step towards a full adaptive implementation is taken in the context of unstructured meshes of simplices with variable order p in space. Both assumptions lead to desirable properties of shape functions like symmetry, p-hierarchy and simple coupling of elements. In a first step it is demonstrate...