Goal-oriented mesh adaptation for flux-limited approximations to steady hyperbolic problems

[摘要] 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. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2010-04-15

[效力级别]  Proceedings Paper

[关键词] Steady transport equations;Flux limiting;A posteriori error estimates;Duality argument;Goal-oriented mesh adaptation