Related papers: A fully discrete numerical control method for the …
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…
We construct a fully discrete numerical scheme that is linear, decoupled, and unconditionally energy stable, and analyze its optimal error estimates for the Cahn-Hilliard-Navier-Stokes equations. For time discretization, we employ the two…
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures…
In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of various classes of damped nonlinear wave equations. Specifically, stabilization the zero steady state solution of initial boundary value…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
We propose and analyze a monotone finite element method for an elliptic distributed optimal control problem constrained by a convection-diffusion-reaction equation in the convection-dominated regime. The method is based on the edge-averaged…
In this paper we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well-posedness…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
In this article, we develop a fully discrete numerical scheme for the one-dimensional (1D) and two-dimensional (2D) viscous Burgers equations with nonlinear Neumann boundary feedback control. The temporal discretization employs a…