An rp-version of the finite element method for physically non-linear problems

In this paper we present an rp-discretization strategy for physically non-linear problems that is based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally, whereas the r-method moves the nodes of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to take the loss of regularity which arises along the shape of the plastic front into account. Numerical examples will demonstrate that this approach leads to more accurate results.     «

In this paper we present an rp-discretization strategy for physically non-linear problems that is based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally, whereas the r-method moves the nodes of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to t...     »