Related papers: A stochastic Galerkin method for optimal Dirichlet…
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving…
The generalized polynomial chaos method is applied to the Buckley-Leverett equation. We consider a spatially homogeneous domain modeled as a random field. The problem is projected onto stochastic basis functions which yields an extended…
We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error…
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent…
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these…
This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…
This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized…
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
This article presents a new primal-dual weak Galerkin method for second order elliptic equations in non-divergence form. The new method is devised as a constrained $L^p$-optimization problem with constraints that mimic the second order…
In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…
In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…
This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
This paper deals with a family of stochastic control problems in Hilbert spaces which arises in typical applications (such as boundary control and control of delay equations with delay in the control) and for which is difficult to apply the…