Name
Title | ||
|---|---|---|
An Adaptive FEM for the Pointwise Tracking Optimal Control Problem of the Stokes Equations. |
Abstract | ||
|---|---|---|
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost functional that involves point evaluations of the velocity field that solves the state equations. This leads to an adjoint problem with a linear combination of Dirac measures as a forcing term and whose solution exhibits reduced regularity properties. We also consider constraints on the control variable. The proposed a posteriori error estimator can be decomposed as the sum of four contributions: three contributions related to the discretization of the state and adjoint equations and another contribution that accounts for the discretization of the control variable. On the basis of the devised a posteriori error estimator, we design a simple adaptive strategy that illustrates our theory and exhibits a competitive performance. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/18M1222363 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
linear-quadratic optimal control problem,Stokes equations,a posteriori error estimates,Dirac measures,Muckenhoupt weights,weighted estimates,maximum-norm estimates | Mathematical optimization,Optimal control,Muckenhoupt weights,A priori and a posteriori,Finite element method,Mathematics,Pointwise,Estimator | Journal |
Volume | Issue | ISSN |
41 | 5 | 1064-8275 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alejandro Allendes | 1 | 4 | 3.92 |
| Francisco Fuica | 2 | 0 | 1.01 |
| Enrique Otárola | 3 | 86 | 13.91 |
| Daniel Quero | 4 | 0 | 1.35 |