THE H-P VERSION OF THE FINITE-ELEMENT METHOD FOR PROBLEMS WITH INTERFACES

Regularities of the solutions of interface problems in two dimensions are described in the frame of the weighted Sobolev spaces and countabl y normed spaces. Based upon the regularity of solutions the geometric meshes and the distribution of polynomial degrees are properly designe d so that the h-p version of the finite element method for interface p roblems can lead to the exponential rate of convergence. Numerical res ults on an elliptic equation with interfaces are presented. The optima l mesh factor, optimal degree factors, and optimal layer factors of th e geometric mesh in neighbourhoods of singular points having varied in tensities are discussed from both theoretical and practical point of v iew.