.Includes index

.Includes bibliographical references (p. 337-347)

Examples and Classification of PDE's -- Classification of PDE's -- Well-posed problems -- The Maximum Principle -- Corollaries -- Finite Difference Methods -- Discretization -- Discrete maximum principle -- A Convergence Theory for Difference Methods -- Consistency -- Local and global error -- Limits of the convergence theory -- Conforming Finite Elements -- Sobolev Spaces -- Introduction to Sobolev spaces -- Friedrichs' inequality -- Possible singularities of H[superscript 1] functions -- Compact imbeddings -- Variational Formulation of Elliptic Boundary-Value Problems of Second Order -- Variational formulation -- Reduction to homogeneous boundary conditions -- Existence of solutions -- Inhomogeneous boundary conditions -- The Neumann Boundary-Value Problem. A Trace Theorem -- Ellipticity in H[superscript 1] -- Boundary-value problems with natural boundary conditions -- Neumann boundary conditions -- Mixed boundary conditions -- Proof of the trace theorem -- Practical consequences of the trace theorem -- The Ritz-Galerkin Method and Some Finite Elements -- Model problem -- Some Standard Finite Elements -- Requirements on the meshes -- Significance of the differentiability properties -- Triangular elements with complete polynomials -- Remarks on C[superscript 1] elements -- Bilinear elements -- Quadratic rectangular elements -- Affine families -- Choice of an element -- Approximation Properties -- The Bramble-Hilbert lemma -- Triangular elements with complete polynomials -- Bilinear
.quadrilateral elements -- Inverse estimates