A POSTERIORI ERROR ESTIMATION FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM INVOLVING THE GENERALIZED OSEEN EQUATIONS

作者：Allendes, Alejandro^*; Otarola, Enrique; Rankin, Richard

来源：SIAM Journal on Scientific Computing, 2018, 40(4): A2200-A2233.

DOI：10.1137/17M1139631

• linear-quadratic optimal control problems
• generalized Oseen equations
• Brinkman equations
• Stokes equations
• a posteriori error estimators
• stabilized adaptive finite element methods

We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples.

• 出版日期2018
• 单位宁波诺丁汉大学