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.
