Compatible Spatial Discretizations (Google eBook)

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Douglas N. Arnold, Pavel B. Bochev, Richard B. Lehoucq, Roy A. Nicolaides, Mikhail Shashkov
Springer Science & Business Media, Jan 26, 2007 - Mathematics - 247 pages
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This IMA Volume in Mathematics and its Apphcations COMPATIBLE SPATIAL DISCRETIZATIONS contains papers presented at a highly successful IMA Hot Topics Work shop: Compatible Spatial Discretizations for Partial Differential Equations. The event which was held on May 11-15, 2004 was organized by Douglas N. Arnold (IMA, University of Minnesota), Pavel B. Bochev (Computa tional Mathematics and Algorithms Department, Sandia National Labora tories), Richard B. Lehoucq (Computational Mathematics and Algorithms Department, Sandia National Laboratories), Roy A. Nicolaides (Depart ment of Mathematical Sciences, Carnegie-Mellon University), and Mikhail Shashkov (MS-B284, Group T-7, Theoretical Division, Los Alamos Na tional Laboratory). We are grateful to all participants and organizers for making this a very productive and stimulating meeting, and we would like to thank the organizers for their role in editing this proceeding. We take this opportunity to thank the National Science Foundation for its support of the IMA and the Department of Energy for providing additional funds to support this workshop. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE In May 2004 over 80 mathematicians and engineers gathered in Min neapolis for a "hot topics" IMA workshop to talk, argue and conjecture about compatibility of spatial discretizations for Partial Differential Equa tions. We define compatible, or mimetic, spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum princi ples.
  

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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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