相关论文: A max-plus finite element method for solving finit…

We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition…

In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

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…

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.…

For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators,…

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…

We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary control. The ecological predator-prey optimal control model…

In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor-Hood elements, under the assumption of the…

We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…

Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…

We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…

We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process.…

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.

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, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…