Decoupled mixed element methods for fourth order elliptic control problems with control constraints
Affiliation of Author(s):
理学院
Journal:
Numerical Mathematics-Theory Methods and Applications
Key Words:
Fourth order elliptic equation, optimal control problem, decoupled mixed element method, Lagrange element, nonconforming Crouzeix-Raviart element, a priori error estimates.
Abstract:
In this paper, we study the finite element methods for distributed optimal control problems governed by the biharmonic operator. Motivated from reducing the regularity of solution space, we use the decoupled mixed element method which was used to approximate the solution of biharmonic equation to solve the fourth order optimal control problems. Two finite element schemes, i.e., Lagrange conforming element combined with full control discretization and the nonconforming Crouzeix-Raviart element combined with variational control discretization, are used to discretize the decoupled optimal control system. The corresponding a priori error estimates are derived under appropriate norms which are then verified by extensive numerical experiments.
Paper Publications
