What question did this study set out to answer?

To establish a goal-oriented framework for a posteriori error estimation and adaptive mesh design in finite element methods using optimal control duality techniques.

May 1, 2001Acta Numerica

An optimal control approach to a posteriori error estimation in finite element methods

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To establish a goal-oriented framework for a posteriori error estimation and adaptive mesh design in finite element methods using optimal control duality techniques.
Coupled duality principles from optimal control with Galerkin orthogonality to replace unknown global stability constants with local sensitivity factors.
Computed dual-weighted residuals by approximately solving an auxiliary linear adjoint problem corresponding to specific target quantities of physical interest.
Formulated adaptive mesh refinement algorithms across elliptic, parabolic, and hyperbolic models, testing them on viscous fluid flow, reactive flow, elasto-plasticity, and radiative transfer.
Enabled direct, reliable error bounds for specific physical quantities rather than relying on uninformative global energy or L2 norms.
Established an economical feedback process that guides local mesh refinement and coarsening tailored strictly to user-defined computational targets.
Demonstrated robust, goal-oriented error control across diverse engineering disciplines, including fluid dynamics and structural mechanics.

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Implication

Methodological survey demonstrates duality-based error control for finite element methods, highlighting targeted adaptive mesh refinement across complex physical systems.

Cite This Study

Becker et al. (2001) studied this question.

synapsesocial.com/papers/69debb1d40ea06567955940e https://doi.org/10.1017/s0962492901000010

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Implication

Methodological survey demonstrates duality-based error control for finite element methods, highlighting targeted adaptive mesh refinement across complex physical systems.

An optimal control approach to a posteriori error estimation in finite element methods

Key Points

Discussion

Implication

Cite This Study

An optimal control approach to a posteriori error estimation in finite element methods

Key Points

Discussion

Implication

Cite This Study