The efficiency of the p-version finite element method

The p-version of the finite element method is now commonly considered to be a very accurate discretization method for linear elliptic partial differential equations, but many researchers still doubt the efficiency of this method, when compared to the classical h-version and applied to more complex problems. This paper will first discuss some general considerations about the efficiency of a numerical method and then present results on an evaluation of the p-version. It will be shown, that there are many special techniques being applicable to the p-version, yielding a well-performing and robust method. This will be demonstrated on several examples, including nonlinear problems and a parallel implementation on a workstation cluster. A client-server software structure for an efficient integration of CAD and FEA using a strict separation of geometric and non-geometric aspects will also be outlined.     «

The p-version of the finite element method is now commonly considered to be a very accurate discretization method for linear elliptic partial differential equations, but many researchers still doubt the efficiency of this method, when compared to the classical h-version and applied to more complex problems. This paper will first discuss some general considerations about the efficiency of a numerical method and then present results on an evaluation of the p-version. It will be shown, that there a...     »