Related papers: An Adaptive Method for Optimal Control Problems Co…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…
In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology…
We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…