hp Finite Element Methods for Singular Perturbations 1.Introduction Part I: Finite Element Approximation 2. hp FEM for Reaction Diffusion Problems: Principal Results 3. hp Approximation Part II: Regularity in Countably Normed Spaces 4. The Countably Normed Spaces blb e 5. Regularity Theory in Countably Normed Spaces Part III: Regularity in Terms of Asymptotic Expansions 6. Exponentially Weighted Countably Normed Spaces Appendix References Index. Many partial differential equations arising in practice are parameter dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics convection diffusion problems in fluid mechanics and equations arising in semi conductor device modelling. Common features of these problems are layers and in the case of non smooth geometries corner singularities. Mesh design principles for the efficient approximation of both features by the hp version of the finite element method (hp FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains robust exponential convergence of the hp FEM based on these mesh design principles is established rigorously.