Error estimation and adaptation for functional outputs in time-dependent flow problems

DOI10.1016/j.jcp.2009.09.034zbMath1355.76046OpenAlexW2024743096MaRDI QIDQ2655695

Dimitri J. Mavriplis, Karthik Mani

Publication date: 25 January 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.09.034

zbMATH Keywords

a posteriori error estimationtemporal adaptationunsteady adjoint method

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection-dominated flows ⋮ Adjoint-based estimation and control of spatial, temporal and stochastic approximation errors in unsteady flow simulations ⋮ A hybridized discontinuous Galerkin method on mapped deforming domains ⋮ An efficient adaptive mesh refinement (AMR) algorithm for the discontinuous Galerkin method: applications for the computation of compressible two-phase flows ⋮ Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains ⋮ PDE-constrained optimization with error estimation and control ⋮ Output-based error estimation and mesh adaptation for unsteady turbulent flow simulations ⋮ Output-based space-time mesh optimization for unsteady flows using continuous-in-time adjoints ⋮ Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids ⋮ Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form ⋮ Output-based space-time mesh adaptation for the compressible Navier-Stokes equations ⋮ Goal-oriented a posteriori error estimation for finite volume methods

Uses Software

• KINSOL
• PVODE

Cites Work

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• The optimal control of unsteady flows with a discrete adjoint method
• Adjoint-based error estimation and grid adaptation for functional outputs: Application to two-dimensional, inviscid, incompressible flows
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• Grid adaptation for functional outputs: application to two-dimensional inviscid flows
• A posteriori error analysis for stabilised finite element approximations of transport problems
• Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows.
• Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement
• Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes
• Space-Time Error Representation and Estimation in Navier-Stokes Calculations
• Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• A Posteriori Error Estimation and Global Error Control for Ordinary Differential Equations by the Adjoint Method

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