Automated Goal-Oriented Error Control I: Stationary Variational Problems

Automated Goal-Oriented Error Control I: Stationary Variational Problems

This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in ...

Goal-oriented a posteriori error estimates for transport problems

Some aspects of goal-oriented a posteriori error estimation are addressed in the context of steady convection-diffusion equations. The difference between the exact and approximate values of a linear target functional is expressed in terms of integrals that depend on the solutions to the primal and dual problems. Gradient averaging techniques are employed to separate the element residual and dif...

Goal-oriented error estimation for fast approximations of nonlinear problems

On goal-oriented adaptivity for elliptic optimal control problems

The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of inte...

New bounding techniques for goal-oriented error estimation applied to linear problems