Partial Differential Equations: Modelling and Numerical Simulation

Part I. Discontinuous Galerkin and Mixed Finite Element Methods. 1. Discontinuous Galerkin Methods. 2. Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations. 3. On the Numerical Solution of the Elliptic Monge--Amp?re Equation in Dimension Two: A Least-Squares Approach. Part II. Linear and Nonlinear Hyperbolic Problems. 1. Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions. 2. Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics. 3. The von Neumann Triple Point Paradox. Part III. Domain Decomposition Methods. 1. A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients. 2. Domain Decomposition and Electronic Structure Computations: A Promising Approach. Part IV. Free Surface, Moving Boundaries and Spectral Geometry Problems. 1. Numerical Analysis of a Finite Element/Volume Penalty Method. 2. A Numerical Method for Fluid Flows with Complex Free Surfaces. 3. Modelling and Simulating the Adhesion and Detachment of Chondrocytes in Shear Flow. Part V. Inverse Problems. 1. A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions. 2. Reduced-Order Modelling of Dispersion. Part VI. Finance (Option Pricing)