Grid adaptation for functional outputs: application to two-dimensional inviscid flows

By D. Venditti, David L. Darmofal. 2002

380 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ed132d8e31e907eabd42da953eb46e211a4d21de

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows (2003, methodology): “Unlike the remaining error terms, the correction term is computable and generally approximates the leading order error in the functional to high accuracy (for example, see the functional convergence results in [21,40,51,52]).”
An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids (2004, background): “The test cases examined in [27,28], and [30–32] clearly demonstrate the potential of using such an approach to grid adaptation.”
Adjoint and defect error bounding and correction for functional estimates (2003, background): “Note that an estimate based on the alternative dual representation of the remainder in (6) would appear to be only O(h(4)).”
Anisotropic mesh adaptation in computational fluid dynamics: application to the advection-diffusion-reaction and the Stokes problems (2004, background): “…triangular elements, i.e., not just their diameter but also their aspect ratio and orienta the other hand, the introduction of the dual problem allows usto control suitable functionals of the discretizati error, e.g., the lift and drag around bodies in external flows, mean and local values, etc.”
Optimal Control and Numerical Adaptivity for Advection-Diffusion Equations (2005, methodology): “We propose the following quadratic reconstruction method, that can be applied for a generic PDE solution v: • compute the generic numerical solution vh by linear finite elements on the triangular grid Th; • refine uniformly the mesh Th, dividing each element in four new elements, to obtain the grid ”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “Thus, in practice, the approach taken in finite volume applications has been to adapt on the remaining error while including the computable correction in the estimate of the output [66].”