Compatible Spatial Discretizations [Hardcover]

The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.

Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions.- Differential Complexes and Stability of Finite Element Methods I. The de Rham Complex.- Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex.- On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems.- Principles of Mimetic Discretizations of Differential Operators.- Compatible Discretizations for Eigenvalue Problems.- Conjugated Bubnov-Galerkin Infinite Element for Maxwell Equations.- Covolume Discretization of Differential Forms.- Mimetic Reconstruction of Vectors.- A Cell-Centered Finite Difference Method on Quadrilaterals.- Development and Application of Compatible Discretizations of Maxwells Equations.

The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science.

Compatible spatial discretizations are those lCŽ