Compatible Spatial Discretizations için kapak resmi
Başlık:
Compatible Spatial Discretizations
Dil:
English
ISBN:
9780387380346
Yayın Bilgileri:
New York, NY : Springer New York, 2006.
Fiziksel Tanımlama:
XIV, 247 p. online resource.
Seri:
The IMA Volumes in Mathematics and its Applications, 142
İçerik:
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 Maxwell’s Equations.
Özet:
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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Özet

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.


İçindekiler

Foreword
Preface
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
Differential 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 Maxwell's Equations