Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
Affiliation of Author(s):
理学院
Journal:
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Key Words:
Optimal control problem
Stokes equations
Control constraints
Adaptive nonconforming finite element
method
Convergence and quasi-optimality
Abstract:
This paper aims at proving the convergence and quasi-optimality of an adaptive nonconforming finite element method for Stokes distributed control problems with pointwise
control constraints. Nonconforming P1/P0 pair (Crouzeix–Raviart elements) and variational discretization are used to approximate the state equation and the control variable,
respectively. A posteriori error estimates with upper and lower bounds are first derived
for the state and adjoint variables. Then we prove the contraction property for the sum
of the energy error of the state and adjoint state and the scaled error estimator on
two consecutive adaptive meshes. The resulting linear convergence is finally used to
show the quasi-optimal convergence rate of the adaptive algorithm. Additionally, some
numerical results are provided to support our theoretical analysis
Paper Publications
