Paper Info
Title
Goal-oriented mesh adaptation for flux-limited approximations to steady hyperbolic problems
Abstract
The development of adaptive numerical schemes for steady transport equations is addressed. A goal-oriented error estimator is presented and used as a refinement criterion for conforming mesh adaptation. The error in the value of a linear target functional is measured in terms of weighted residuals that depend on the solutions to the primal and dual problems. The Galerkin orthogonality error is taken into account and found to be important whenever flux or slope limiters are activated to enforce monotonicity constraints. The localization of global errors is performed using a natural decomposition of the involved weights into nodal contributions. A nodal generation function is employed in a hierarchical mesh adaptation procedure which makes each refinement step readily reversible. The developed simulation tools are applied to a linear convection problem in two space dimensions.
Year
DOI
Venue
2010
10.1016/j.cam.2009.07.026
J. Computational Applied Mathematics
Keywords
Field
DocType
refinement criterion,galerkin orthogonality error,steady hyperbolic problem,flux-limited approximation,global error,linear convection problem,goal-oriented mesh adaptation,goal-oriented error estimator,hierarchical mesh adaptation procedure,nodal generation function,linear target,nodal contribution,mesh adaptation,dual problem,generating function,transport equation,goal orientation
Mathematical optimization,Linear form,Mathematical analysis,Galerkin method,Orthogonality,Decomposition method (constraint satisfaction),Numerical analysis,Partial differential equation,Mathematics,Estimator,Hyperbolic partial differential equation
Journal
Volume
Issue
ISSN
233
12
0377-0427
Citations 
PageRank 
References 
1
0.37
8
Authors
2
Name
Order
Citations
PageRank
Dmitri Kuzmin116723.90
Matthias Möller261.44