The h-p Version of Finite Element Method in R3: Theory and Algorithm

This paper gives a precise description of regularities of solutions and their derivatives of all orders for elliptic problems on polyhedral domains in the frame of the countably normed spaces with weighted Ck-norms in neighborhoods of vertices, edges and vertex-edges. Under the guidance of the regularity theory, the geometric meshes and P-Q distribution (bilinear-linear or linear-uniform) of element degrees are designed accordingly in each of singular neighborhoods. The algorithms combining the geometric mesh and corresponding P-Q distribution of element degree achieve the exponential convergence and efficiency of computation. The performance of the h, p and h-p versions for a benchmark elasticity problem on a polyhedral domain is given and analysed.