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   Articles with "discontinuous galerkin" as a keyword



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A high‐order discontinuous Galerkin method for the incompressible Navier‐Stokes equations on arbitrary grids

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recommendations! Published in 2019 at "International Journal for Numerical Methods in Fluids"

DOI: 10.1002/fld.4718

Abstract: A high‐order discontinuous Galerkin (DG) method is proposed in this work for solving the two‐dimensional steady and unsteady incompressible Navier‐Stokes (INS) equations written in conservative form on arbitrary grids. In order to construct the interface… read more here.

Keywords: discontinuous galerkin; arbitrary grids; method; high order ... See more keywords
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Discontinuous Galerkin finite element method applied to the coupled unsteady Stokes/Cahn‐Hilliard equations

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recommendations! Published in 2019 at "International Journal for Numerical Methods in Fluids"

DOI: 10.1002/fld.4720

Abstract: Two-phase flows driven by the interfacial dynamics are studied by tracking implicitly interfaces in the framework of the Cahn-Hilliard theory. The fluid dynamics is described by the Stokes equations with an additional source term in… read more here.

Keywords: finite element; discontinuous galerkin; galerkin finite; equation ... See more keywords
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Development of a nonconservative discontinuous Galerkin formulation for simulations of unsteady and turbulent flows

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recommendations! Published in 2020 at "International Journal for Numerical Methods in Fluids"

DOI: 10.1002/fld.4785

Abstract: In this paper, discontinuous Galerkin (DG) discretization schemes for Navier‐Stokes equations of a nonconservative form was proposed, in which the constitutional equation for energy conservation is written in terms of pressure. The primary focus is… read more here.

Keywords: discontinuous galerkin; development nonconservative; nonconservative discontinuous; formulation ... See more keywords
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Solvability of the fractional Volterra‐Fredholm integro differential equation by hybridizable discontinuous Galerkin method

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5821

Abstract: This article proves the existence and uniqueness of the solution obtained by the hybridizable discontinuous Galerkin (HDG) method of the fractional Volterra‐Fredholm integro differential equation. The method based on local solvers and transmission condition is… read more here.

Keywords: discontinuous galerkin; volterra fredholm; method; equation ... See more keywords
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Analysis of a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase flow in porous media with dynamic capillarity effects

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recommendations! Published in 2017 at "International Journal for Numerical Methods in Engineering"

DOI: 10.1002/nme.5526

Abstract: ShellNWO/FOM CSER (project 14CSER016); NWO Visitors Grant 040.11.499; ResearchFoundation - Flanders FWO, Odysseus project G0G1316N; Statoil Akademia grant read more here.

Keywords: analysis linearization; linearization scheme; discontinuous galerkin; interior penalty ... See more keywords
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Augmented Lagrangian approach to deriving discontinuous Galerkin methods for nonlinear elasticity problems

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recommendations! Published in 2022 at "International Journal for Numerical Methods in Engineering"

DOI: 10.1002/nme.7039

Abstract: We use the augmented Lagrangian formalism to derive discontinuous Galerkin (DG) formulations for problems in nonlinear elasticity. In elasticity, stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices in Newton's… read more here.

Keywords: discontinuous galerkin; elasticity; lagrangian approach; nonlinear elasticity ... See more keywords
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A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form

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recommendations! Published in 2020 at "Numerische Mathematik"

DOI: 10.1007/s00211-020-01160-w

Abstract: We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First, we consider the… read more here.

Keywords: stable discontinuous; energy; discontinuous galerkin; method ... See more keywords
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Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations

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recommendations! Published in 2021 at "Numerische Mathematik"

DOI: 10.1007/s00211-021-01183-x

Abstract: We provide a framework for the analysis of the direct discontinuous Galerkin (DDG) methods for multi-dimensional convection-diffusion equations subject to various boundary conditions. A key tool is the global projection constructed by the DDG scheme… read more here.

Keywords: analysis direct; convection diffusion; discontinuous galerkin; direct discontinuous ... See more keywords
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Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations

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recommendations! Published in 2021 at "Numerische Mathematik"

DOI: 10.1007/s00211-021-01209-4

Abstract: We propose and analyze a class of robust, uniformly high-order accurate discontinuous Galerkin (DG) schemes for multidimensional relativistic magnetohydrodynamics (RMHD) on general meshes. A distinct feature of the schemes is their physical-constraint-preserving (PCP) property, i.e.,… read more here.

Keywords: physical constraint; multidimensional relativistic; discontinuous galerkin; constraint ... See more keywords
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Performance and Scalability Improvements for Discontinuous Galerkin Solutions to Conservation Laws on Unstructured Grids

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recommendations! Published in 2017 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-016-0249-y

Abstract: This paper presents a computational framework developed to improve both the serial and parallel performance of two dimensional, unstructured, discontinuous Galerkin (DG) solutions to hyperbolic conservation laws. The coding techniques employed factor in advancements trending… read more here.

Keywords: galerkin solutions; discontinuous galerkin; performance; conservation laws ... See more keywords
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Stability of Nonlinear Convection–Diffusion–Reaction Systems in Discontinuous Galerkin Methods

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recommendations! Published in 2017 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-016-0256-z

Abstract: In this work we provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection–reaction–diffusion systems. We provide a partial linearization under which a sufficient… read more here.

Keywords: discontinuous galerkin; nonlinear convection; reaction; galerkin methods ... See more keywords