Elliptic Differential Equations : Theory and Numerical Treatment 1 Partial Differential Equations and Their Classification Into Types 2 The Potential Equation 3 The Poisson Equation 4 Difference Methods for the Poisson Equation 5 General Boundary Value Problems 6 Tools from Functional Analysis 7 Variational Formulation 8 The Method of Finite Elements 9 Regularity 10 Special Differential Equations 11 Eigenvalue Problems 12 Stokes Equations This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite element methods which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle point problem taking into account its relevance to applications in fluid dynamics