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A triangular cutcell adaptive method for highorder discretizations of the compressible Navier–Stokes equations
, 2007
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OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results
"... Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on the ..."
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Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for Computational Fluid Dynamics (CFD) applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fullydiscrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in output error estimation using the finite volume method and the finite element method. Recent adaptive results from a variety of applications show the power of outputbased adaptive methods for improving the robustness of CFD computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I
Review of OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
"... Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on th ..."
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Cited by 3 (1 self)
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Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in outputerror estimation using the finite volume method and the finite element method. Techniques for adapting meshes using outputerror indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynoldsaveraged Navier–Stokes applications show the power of outputbased adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I.
On a posteriori pointwise error estimation using adjoint temperature and Lagrange remainder
, 2005
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Computing and Information SYMMETRIC INTERIOR PENALTY DG METHODS FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS II: GOAL–ORIENTED A POSTERIORI ERROR ESTIMATION
"... Abstract. In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier– Stokes equations. In particular, we consider the a posteriori error ana ..."
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Abstract. In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier– Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented. Key Words. Discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier–Stokes equations 1.
ARTICLE IN PRESS 2 On a posteriori pointwise error estimation using
, 2004
"... 10 The pointwise estimation of heat conduction solution as a function of truncation error of a finite difference scheme is 11 addressed. The truncation error is estimated using a Taylor series with the remainder in the Lagrange form. The con12 tribution of the local error to the total pointwise err ..."
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10 The pointwise estimation of heat conduction solution as a function of truncation error of a finite difference scheme is 11 addressed. The truncation error is estimated using a Taylor series with the remainder in the Lagrange form. The con12 tribution of the local error to the total pointwise error is estimated via an adjoint temperature. It is demonstrated that 13 the results of numerical calculation of the temperature at an observation point may thus be refined via adjoint error 14 correction and that an asymptotic error bound may be found.
Refinement of A Posteriori pointwise Error Estimation for Compressible Fluid Flows using adjoint parameters and Lagrange
"... The pointwise error of a finitedifference calculation of supersonic flow is considered. The local truncation error is determined using a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated ..."
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The pointwise error of a finitedifference calculation of supersonic flow is considered. The local truncation error is determined using a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated via adjoint parameters. It is demonstrated by numerical tests that the results of numerical calculation of gasdynamics parameter at an observation point may be refined and an error bound may be estimated. The results of numerical tests for a case of parabolized NavierStokes (PNS) equations are presented as an illustration of the proposed method. 1. Introduction. There are several approaches for a posteriori error estimation in the finiteelement analysis [14] most of which are specific for elliptic equations. Nevertheless, an option based on the adjoint equations is not limited by the methods of finiteelement analysis and is applicable for any type of equations. In Refs. [59] a posteriori error estimation is obtained for NavierStokes and Euler equations. In these works the Galerkin