English
Related papers

Related papers: A hybridizable discontinuous Galerkin method for t…

200 papers

We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state,…

Numerical Analysis · Mathematics 2018-06-04 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

This paper proposes an interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface problems in two and three dimensions. The method uses piecewise linear polynomials for the…

Numerical Analysis · Mathematics 2020-12-08 Yihui Han , Xiao-Ping Wang , Xiaoping Xie

Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the…

Numerical Analysis · Mathematics 2020-01-24 Guosheng Fu , Christoph Lehrenfeld , Alexander Linke , Timo Streckenbach

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…

Numerical Analysis · Mathematics 2024-11-26 Shipra Gupta , Amiya Kumar Pani , Sangita Yadav

In this paper, we present a hybridized discontinuous Galerkin (HDG) method for Poisson-type problems with sign-changing coefficients. We introduce a sign-changing stabilization parameter that results in a stable HDG method independent of…

Numerical Analysis · Mathematics 2019-11-12 Jeonghun J. Lee , Sander Rhebergen

This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Richard Schussnig , Niklas Fehn , Douglas Ramalho Queiroz Pacheco , Martin Kronbichler

The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is…

Numerical Analysis · Mathematics 2019-08-16 Ruben Sevilla , Matteo Giacomini , Alexandros Karkoulias , Antonio Huerta

We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimal a priori…

Numerical Analysis · Mathematics 2023-03-20 A. Cesmelioglu , J. J. Lee , S. Rhebergen

In this work, a novel analysis of a hybrid discontinuous Galerkin method for the Helmholtz equation is presented. It uses wavenumber, mesh size and polynomial degree independent stabilisation parameters leading to impedance traces between…

Numerical Analysis · Mathematics 2023-07-11 Michael Leumüller , Joachim Schöberl

We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes equations are discretized using a divergence-free HDG…

Numerical Analysis · Mathematics 2021-03-30 Guosheng Fu

Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and…

Computational Engineering, Finance, and Science · Computer Science 2020-06-24 Luca Berardocco , Martin Kronbichler , Volker Gravemeier

We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous media. In particular we apply the HDG methodology to the recently introduced reinterpreted discrete…

Numerical Analysis · Mathematics 2023-03-01 Guosheng Fu , Yang Yang

In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with the hydrodynamic model for the conduction-band electrons in metals. By means of a static…

Computational Physics · Physics 2021-03-17 Ferran Vidal-Codina , Ngoc-Cuong Nguyen , Cristian Ciraci , Sang-Hyun Oh , Jaime Peraire

We present a superconvergent hybridizable discontinuous Galerkin (HDG) method for the steady-state incompressible Navier-Stokes equations on general polyhedral meshes. For arbitrary conforming polyhedral mesh, we use polynomials of degree…

Numerical Analysis · Mathematics 2015-11-30 Weifeng Qiu , Ke Shi

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate…

Numerical Analysis · Mathematics 2016-06-29 Binjie Li , Xiaoping Xie , Shiquan Zhang

The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy's law).…

Numerical Analysis · Mathematics 2020-07-15 Yanxia Qian , Shuonan Wu , Fei Wang

Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…

Numerical Analysis · Mathematics 2018-02-01 Sander Rhebergen , Garth N. Wells

This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop…

Computational Engineering, Finance, and Science · Computer Science 2025-07-31 Vahid Badrkhani , Marco F. P. ten Eikelder , Dominik Schillinger

Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as…

Numerical Analysis · Mathematics 2019-10-02 Gabriel R. Barrenechea , Michał Bosy , Victorita Dolean , Frédéric Nataf , Pierre-Henri Tournier

We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Sander Rhebergen