Related papers: Space-time Galerkin POD with application in optima…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
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 consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…
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…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
We analyze Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique.…
In this paper we study the approximation of an 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 functions are…
We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis. We show that for linear,…
The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as…
In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only…
We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…