Finite-element approximation of 2D elliptic optimal design

Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems

In this paper, we present a priori error analysis for the finite element discretization of elliptic optimal control problems, where a finite dimensional control variable enters the Dirichlet boundary conditions. The analysis of finite element approximations of optimization problems governed by partial differential equations is an area of active research, see, e.g., [1, 12, 17, 18]. The consider...

Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adj...

Finite element approximation of fractional order elliptic boundary value problems

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...

The Finite Element Method for 2D elliptic PDEs

Optimal Design of Sandwich Panels Using Multi-Objective Genetic Algorithm and Finite Element Method

Low weight and high load capacity are remarkable advantages of sandwich panels with corrugated core, which make them more considerable by engineering structure designers. It’s important to consider the limitations such as yielding and buckling as design constraints for optimal design of these panels. In this paper, multi-objective optimization of sandwich panels with corrugated core is carried ...