Geometry representation issues associated with p-version finite element computations Original Research Article

This paper addresses issues related to accurate geometry representation for p-version finite elements on curved three-dimensional domains. Specific options to account for domain geometry information during element-level computation are identified. Accuracy requirements on the geometry related approximations to preserve the optimal rate of finite element error convergence for second-order elliptic boundary value problems are given. An element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly during element integrations, or used to construct element-level geometric approximations of required accuracy. Smoothness issues of the rational blends on simplex topologies are discussed and a numerical example based on the solution of Poissonʹs equation in three dimensions is presented to illustrate the impact of the rational blends on the optimal rate of finite element error convergence.