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A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space ApproximationWe consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.
Document ID
20000064581
Document Type
Conference Paper
Authors
Barth, Timothy J. (NASA Ames Research Center Moffett Field, CA United States)
Larson, Mats G. (Chalmers Univ. of Technology Goeteborg, Sweden)
Date Acquired
August 19, 2013
Publication Date
February 1, 2000
Publication Information
Publication: Welcome to the NASA High Performance Computing and Communications Computational Aerosciences (CAS) Workshop 2000
Subject Category
Theoretical Mathematics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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