English
Related papers

Related papers: An HDG Method for Distributed Control of Convectio…

200 papers

We consider a distributed optimal control problem governed by an elliptic convection diffusion PDE, and propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. We use polynomials of degree $k+1$ and $k \ge 0$…

Numerical Analysis · Mathematics 2018-11-27 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…

Numerical Analysis · Mathematics 2019-06-04 Xiao Zhang , Yangwen Zhang , John R. Singler

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state,…

Numerical Analysis · Mathematics 2018-07-25 Xiao Zhang , Yangwen Zhang , John R. Singler

We propose a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a Dirichlet boundary control problem governed by an elliptic convection diffusion PDE. Even without a convection term, Dirichlet boundary…

Numerical Analysis · Mathematics 2018-01-08 Weiwei Hu , Mariano Mateos , John R. Singler , Yangwen Zhang

In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D…

Numerical Analysis · Mathematics 2018-07-25 Weiwei Hu , Mariano Mateos , John R. Singler , Xiao Zhang , Yangwen Zhang

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a \emph{convection dominated} Dirichlet boundary control problem. Dirichlet boundary control problems and convection dominated problems are…

Numerical Analysis · Mathematics 2021-02-01 Gang Chen , John Richard Singler , Yangwen Zhang

We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for…

Numerical Analysis · Mathematics 2021-02-01 Gang Chen , Guosheng Fu , John Richard Singler , Yangwen Zhang

In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…

Numerical Analysis · Mathematics 2013-11-01 Issei Oikawa

We analyze a high order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection-diffusion equation posed in a domain with piecewise-wise $\mathcal{C}^2$ boundary $\partial \Omega$.…

Numerical Analysis · Mathematics 2026-04-02 Esteban Henríquez , Manuel Solano

In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms…

Numerical Analysis · Mathematics 2019-03-12 Gang Chen , Liangya Pi , Liwei Xu , Yangwen Zhang

We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations,…

Numerical Analysis · Mathematics 2017-12-11 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

We analyze families of primal high-order hybridizable discontinuous Galerkin (HDG) methods for solving degenerate (second-order) elliptic problems. One major trouble regarding this class of PDEs concerns its mathematical nature, which may…

Numerical Analysis · Mathematics 2021-06-02 G. Etangsale , M. Fahs , V. Fontaine , A. R. Isa-Abadi

We propose a hybridizable discontinuous Galerkin (HDG) finite element method to approximate the solution of the time dependent drift-diffusion problem. This system involves a nonlinear convection diffusion equation for the electron…

Numerical Analysis · Mathematics 2018-11-27 Gang Chen , Peter Monk , Yangwen Zhang

In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming…

Numerical Analysis · Mathematics 2022-12-13 Issei Oikawa

We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…

Numerical Analysis · Mathematics 2025-06-24 Salim Meddahi

In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG)…

Numerical Analysis · Mathematics 2018-06-20 Siu Wun Cheung , Eric T. Chung

In this work, we propose a novel strategy for the numerical solution of linear convection diffusion equation (CDE) over unfitted domains. In the proposed numerical scheme, strategies from high order Hybridized Discontinuous Galerkin method…

Numerical Analysis · Mathematics 2023-06-02 Haroon Ahmad , Ceren Gürkan

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…

Numerical Analysis · Mathematics 2025-06-17 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

A linear semi-implicit hybridizable discontinuous Galerkin (HDG) scheme is proposed to solve the diffusive Peterlin viscoelastic model, allowing the diffusion coefficient $\ep$ of the conformation tensor to be arbitrarily small. We…

Numerical Analysis · Mathematics 2025-03-12 Sibang Gou , Jingyan Hu , Qi Wang , Feifei Jing , Guanyu Zhou

In this paper, we develop hybridized discontinuous Galerkin (HDG) methods for poroelastic wave equations. We first rewrite the governing equations to a first-order symmetric hyperbolic system in order to use dual mixed formulations for…

Numerical Analysis · Mathematics 2026-05-08 Jeonghun J. Lee , Manuel A. Sanchez
‹ Prev 1 2 3 10 Next ›