The P and Hp Versions of the Nite Element Method for Problems with Boundary Layers

We study the uniform approximation of boundary layer functions exp(?x=d) for x 2 (0; 1), d 2 (0; 1], by the p and hp versions of the nite element method. For the p version (with xed mesh), we prove super-exponential convergence in the range p +1=2 > e=(2d). We also establish, for this version, an overall convergence rate of O(p ?1 p lnp) in the energy norm… (More)