Compatible Spatial Discretizations (Google eBook)

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Springer Science & Business Media, Jan 26, 2007 - Mathematics - 264 pages
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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 that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.
  

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Contents

NUMERICAL CONVERGENCE OF THE MPFA OMETHOD FOR GENERAL QUADRILATERAL GRIDS IN TWO AND THREE DIMENSIONS
1
DIFFERENTIAL COMPLEXES AND STABILITY OF FINITE ELEMENT METHODS I THE DE RHAM COMPLEX
23
THE ELASTICITY COMPLEX
47
ON THE ROLE OF INVOLUTIONS IN THE DISCONTINUOUS GALERKIN DISCRETIZATION OF MAXWELL AND MAGNETOHYDRODYN...
69
PRINCIPLES OF MIMETIC DISCRETIZATIONS OF DIFFERENTIAL OPERATORS
89
COMPATIBLE DISCRETIZATIONS FOR EIGENVALUE PROBLEMS
121
CONJUGATED BUBNOVGALERKIN INFINITE ELEMENT FOR MAXWELL EQUATIONS
143
COVOLUME DISCRETIZATION OF DIFFERENTIAL FORMS
161
MIMETIC RECONSTRUCTION OF VECTORS
173
A CELLCENTERED FINITE DIFFERENCE METHOD ON QUADRILATERALS
189
DEVELOPMENT AND APPLICATION OF COMPATIBLE DISCRETIZATIONS OF MAXWELLS EQUATIONS
209
LIST OF WORKSHOP PARTICIPANTS
235
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