edited by Maurizio Falcone (Università di Roma “La Sapienza”, Italy) & Charalampos Makridakis (University of Crete, Greece)

The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.

• Geometrical Optics and Viscosity Solutions (A-P Blanc et al.)
• Computation of Vorticity Evolution for a Cylindrical Type-II Superconductor Subject to Parallel and Transverse Applied Magnetic Fields (A Briggs et al.)
• A Characterization of the Value Function for a Class of Degenerate Control Problems (F Camilli)
• Some Microstructures in Three Dimensions (M Chipot & V Lécuyer)
• Convergence of Numerical Schemes for the Approximation of Level Set Solutions to Mean Curvature Flow (K Deckelnick & G Dziuk)
• Optimal Discretization Steps in Semi-Lagrangian Approximation of First Order PDEs (M Falcone et al.)
• Convergence Past Singularities to the Forced Mean Curvature Flow for a Modified Reaction-Diffusion Approach (F Fierro)
• The Viscosity/Duality Solutions Approach to Geometric Optics for the Helmholtz Equation (L Gosse & F James)
• Adaptive Grid Generation for Evolutive Hamilton-Jacobi-Bellman Equations (L Grüne)
• Solution and Application of Anisotropic Curvature Driven Evolution of Curves (and Surfaces) (K Mikula)
• An Adaptive Scheme on Unstructured Grids for the Shape-From-Shading Problem (M Sagona & A Seghini)
• On a Posteriori Error Estimation for Constant Obstacle Problems (A Veeser)