Related papers: A new error analysis for parabolic Dirichlet bound…
We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…
Upon the recent development of the quasi-reversibility method for terminal value parabolic problems in \cite{Nguyen2019}, it is imperative to investigate the convergence analysis of this regularization method in the stochastic setting. In…
We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…
We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most $r-1$ in $t$, for $r\ge1$ and with maximum step size~$k$. It is well known that the…
In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that considering a time discretization with a positive step size $h$ an error bound of…
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…
The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
We consider a model initial- and Dirichlet boundary- value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. First, we approximate its solution by the…
In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…
An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. An L2-type discrete fractional-derivative…
We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…
The global null controllability of stochastic semilinear parabolic equations with globally Lipschitz nonlinearities has been addressed in recent literature. However, there are no results concerning their numerical approximation and the…
In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different…
We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…