Grid adaptation for functional outputs: application to two-dimensional inviscid flows
Journal of Computational Physics
Aspects of discontinuous Galerkin methods for hyperbolic conservation laws
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Adjoint and defect error bounding and correction for functional estimates
Journal of Computational Physics
Even-odd goal-oriented a posteriori error estimation for elliptic problems
Applied Numerical Mathematics
"Natural norm" a posteriori error estimators for reduced basis approximations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Adjoint A Posteriori Error Measures for Anisotropic Mesh Optimisation
Computers & Mathematics with Applications
Journal of Computational Physics
Even--odd goal-oriented a posteriori error estimation for elliptic problems
Applied Numerical Mathematics
Adjoint correction and bounding of error using lagrange form of truncation term
Computers & Mathematics with Applications
Review: A posteriori error estimation techniques in practical finite element analysis
Computers and Structures
Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
SIAM Journal on Scientific Computing
An Entropy Adjoint Approach to Mesh Refinement
SIAM Journal on Scientific Computing
Output-based space-time mesh adaptation for the compressible Navier-Stokes equations
Journal of Computational Physics
Predicting goal error evolution from near-initial-information: A learning algorithm
Journal of Computational Physics
Shape optimization of an airfoil in the presence of compressible and viscous flows
Computational Optimization and Applications
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Output error estimation for summation-by-parts finite-difference schemes
Journal of Computational Physics
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
On the impact of boundary conditions on dual consistent finite difference discretizations
Journal of Computational Physics
Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains
Journal of Computational Physics
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
PDE-constrained optimization with error estimation and control
Journal of Computational Physics
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Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasi-one-dimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multi-dimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations.