This book is dedicated to Olivier Pironneau.

"This book is dedicated to Olivier Pironneau.

Discontinuous Galerkin and Mixed Finite Element Methods.- Discontinuous Galerkin Methods.- Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations.- On the Numerical Solution of the Elliptic Monge-Ampère Equation in Dimension Two: A Least-Squares Approach.- Linear and Nonlinear Hyperbolic Problems.- Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions.- Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics.- The von Neumann Triple Point Paradox.- Domain Decomposition Methods.- A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients.- Domain Decomposition and Electronic Structure Computations: A Promising Approach.- Free Surface, Moving Boundaries and Spectral Geometry Problems.- Numerical Analysis of a Finite Element/Volume Penalty Method.- A Numerical Method for Fluid Flows with Complex Free Surfaces.- Modelling and Simulating the Adhesion and Detachment of Chondrocytes in Shear Flow.- Computing the Eigenvalues of the Laplace-Beltrami Operator on the Surface of a Torus: A Numerical Approach.- Inverse Problems.- A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions.- Reduced-Order Modelling of Dispersion.- Finance (Option Pricing).- Calibration of Lévy Processes with American Options.- An Operator Splitting Method for Pricing American Options.