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This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…

Numerical Analysis · Mathematics 2025-08-18 Harpal Singh , Arbaz Khan

We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and…

Numerical Analysis · Mathematics 2017-06-06 Sriramkrishnan Muralikrishnan , Minh-Binh Tran , Tan Bui-Thanh

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…

Numerical Analysis · Mathematics 2020-09-10 Ruben Sevilla , Luca Borchini , Matteo Giacomini , Antonio Huerta

This work is concerned with implementing the hybridizable discontinuous Galerkin (HDG) method to solve the linear anisotropic elastic equation in the frequency domain. First-order formulation with the compliance tensor and Voigt notation…

Analysis of PDEs · Mathematics 2024-04-29 Ha Pham , Florian Faucher , Hélène Barucq

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

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small…

Fluid Dynamics · Physics 2018-12-26 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

We present a stability and error analysis of an embedded-hybridized discontinuous Galerkin (EDG-HDG) finite element method for coupled Stokes--Darcy flow and transport. The flow problem, governed by the Stokes--Darcy equations, is…

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

We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum…

Numerical Analysis · Mathematics 2020-04-22 Juan Manzanero , Gonzalo Rubio , David A. Kopriva , Esteban Ferrer , Eusebio Valero

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

We introduce new hybridizable discontinuous Galerkin (HDG) methods for solving the two-dimensional vector Laplacian equation under three types of boundary conditions: electric, magnetic, and Dirichlet. The method is formulated on a…

Numerical Analysis · Mathematics 2026-04-08 Bernardo Cockburn , Cristhian Núñez , Manuel A. Sánchez

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

We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative…

Numerical Analysis · Mathematics 2025-04-28 Simone Pescuma , Gwénaël Gabard , Théophile Chaumont-Frelet , Axel Modave

This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework for both…

Computational Physics · Physics 2021-03-17 Niklas Fehn , Johannes Heinz , Wolfgang A. Wall , Martin Kronbichler

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and…

Numerical Analysis · Mathematics 2022-09-07 Jiansong Zhang , Yun Yu , Jiang Zhu , Rong Qin , Yue Yu , Maosheng Jiang

This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…

Numerical Analysis · Mathematics 2022-02-08 Juan M. Cardenas , Manuel Solano

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

In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber…

Numerical Analysis · Mathematics 2024-11-26 Gang Chen , Haijun Wu , Liwei Xu

We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…

Numerical Analysis · Mathematics 2014-09-26 Bernardo Cockburn , Kassem Mustapha

We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the…

Numerical Analysis · Mathematics 2021-12-21 Lorenzo Botti , Francesco Carlo Massa

The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at…

Numerical Analysis · Mathematics 2025-05-08 Ari E. Rappaport , Théophile Chaumont-Frelet , Axel Modave