Related papers: Spacetime finite element methods for control probl…
In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite…
We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error…
In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…
We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regularisation viewpoint of the wave equation in second-order…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…
This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method for incompressible flow problems in moving domains. The…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…
This paper represents a new perspective in understanding the controllability of the Korteweg-de Vries (KdV) equation on unbounded domains. By studying the equation on both the right and left half-line with a single control input, we show…