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A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…

Analysis of PDEs · Mathematics 2026-02-17 Régis Duvigneau

An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…

Numerical Analysis · Mathematics 2019-03-19 Lu Zhang , Thomas Hagstrom , Daniel Appelo

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…

Numerical Analysis · Mathematics 2020-05-06 Andrew R. Winters , David A. Kopriva , Gregor J. Gassner , Florian Hindenlang

This paper develops an hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD) flow. The HDG scheme uses piecewise polynomials of degrees…

Numerical Analysis · Mathematics 2025-01-03 Min Zhang , Zimo Zhu , Qijia Zhai , Xiaoping Xie

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…

Numerical Analysis · Mathematics 2021-11-24 Tuan Anh Dao , Ken Mattsson , Murtazo Nazarov

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen

We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such…

Numerical Analysis · Mathematics 2019-10-23 Peter Monk , Yangwen Zhang

Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyperbolicity of the underlying hyperbolic system. We apply a…

Numerical Analysis · Mathematics 2019-12-20 Jakob Dürrwächter , Thomas Kuhn , Fabian Meyer , Louisa Schlachter , Florian Schneider

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several…

Numerical Analysis · Mathematics 2022-05-16 Johannes Kraus , Philip L. Lederer , Maria Lymbery , Kevin Osthues , Joachim Schöberl

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field,…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,…

Numerical Analysis · Mathematics 2019-03-25 Han Yihui , Xie Xiaoping

We present and analyze a weak Galerkin finite element method for solving the transport-reaction equation in $d$ space dimensions. This method is highly flexible by allowing the use of discontinuous finite element on general meshes…

Numerical Analysis · Mathematics 2020-11-25 Tie Zhang , Shangyou Zhang

The interior penalty discontinuous Galerkin method is applied to solve elliptic equations on either networks of segments or networks of planar surfaces, with arbitrary but fixed number of bifurcations. Stability is obtained by proving a…

Numerical Analysis · Mathematics 2025-12-15 Miroslav Kuchta , Rami Masri , Beatrice Riviere

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 consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a…

Numerical Analysis · Mathematics 2025-07-29 Johannes Kraus , Maria Lymbery , Kevin Osthues

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

In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…

Numerical Analysis · Mathematics 2024-04-26 Efthymios N. Karatzas

This paper deals with the numerical resolution of kinetic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. We focus on the kinetic model considered in [18, 17] where alignment is…

Numerical Analysis · Mathematics 2017-05-24 Francis Filbet , Chi-Wang Shu

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…

Numerical Analysis · Mathematics 2019-11-26 Ruo Li , Zhiyuan Sun , Zhijian Yang

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…

Computational Engineering, Finance, and Science · Computer Science 2018-02-19 Maurice S. Fabien , Matthew G. Knepley , Beatrice M. Riviere