Bq. Guo et Hs. Oh, THE H-P VERSION OF THE FINITE-ELEMENT METHOD FOR PROBLEMS WITH INTERFACES, International journal for numerical methods in engineering, 37(10), 1994, pp. 1741-1762
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.