Results 51 to 60 of about 19,690 (191)

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations [PDF]

Journal of Scientific Computing, 2010
The authors discuss an \(hp\)-local discontinuous Galerkin (LDG) method for parabolic integro-differential equations. Preliminaries, basic results and the LDG method are presented. A priori error estimates for an extended mixed type Ritz-Volterra projection are discussed. Numerical examples are given to illustrate the predicted convergence rates.
PANI, AK, YADAV, S
openaire   +3 more sources

hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. [PDF]

, 2002
In this paper we consider the a posteriori and a priori analysis of hp-discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form. In particular, we discuss the question of error
Harriman, Kathryn, Houston, P., Senior, Bill, Suli, Endre   +3 more
core  

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

, 2017
The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space.
Fehn, Niklas, Kronbichler, Martin, Wall, Wolfgang A.   +2 more
core   +1 more source

Efficient Energy‐Stable Discontinuous Galerkin Scheme for the Non‐Isothermal Cahn–Hilliard–Navier–Stokes Two‐Phase Fluid Flow System

International Journal for Numerical Methods in Engineering, Volume 127, Issue 7, 15 April 2026.
ABSTRACT In this article, we propose a novel numerical framework for the non‐isothermal Cahn–Hilliard–Navier–Stokes two‐phase flow system, which couples the incompressible Navier–Stokes equations, the Cahn–Hilliard phase‐field equation, and the heat transport equation to capture temperature‐dependent two‐phase flow dynamics.
Guang‐An Zou, Meiting Wang, Kejia Pan, Yin Yang, Xiaofeng Yang   +4 more
wiley   +1 more source

Distributional derivatives and stability of discontinuous Galerkin finite element approximation methods

Electronic Journal of Differential Equations, 2016
The goal of this article is to explore and motivate stabilization requirements for various types of discontinuous Galerkin (DG) methods. A new approach for the understanding of DG approximation methods for second order elliptic partial differential ...
Thomas Lewis
doaj  

Application of High‐Order Direct Flux Reconstruction and Stiffness‐Resilient Time Integration to Simulations of Idealized Atmospheric Flows

International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 448-468, April 2026.
The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault, Christopher Subich, Shoyon Panday, Martin Charron, Vincent Magnoux, Valentin Dallerit, Mayya Tokman   +6 more
wiley   +1 more source

An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity

Results in Applied Mathematics, 2019
It is now a well known fact that hybridizable discontinuous Galerkin for nonlinear elasticity may not converge to the exact solution if their inter-element jumps are not properly penalized or, equivalently, if the values of their stabilization function ...
Bernardo Cockburn, Jiguang Shen
doaj   +1 more source

Explicit local time-stepping methods for time-dependent wave propagation [PDF]

, 2012
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations.
Grote, Marcus, Mitkova, Teodora
core   +1 more source

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

, 2018
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 value, $\mathrm{
Arndt, Arnold, Bassi, Beck, Beck, Brown, Cantwell, Carton de Wiart, Carton de Wiart, Chapelier, Del Alamo, Fehn, Fehn, Fehn, Fernandez, Fischer, Flad, Flad, Franciolini, Gassner, Guermond, Hager, Hartmann, Hesthaven, Hillewaert, Hindenlang, Joshi, Karniadakis, Kennedy, Kirby, Kopriva, Krank, Krank, Kronbichler, Kronbichler, Kronbichler, Kronbichler, Kubatko, Mengaldo, Moser, Moura, Orszag, Pazner, Steinmoeller, Taylor, Toulorge, Uranga, Vos, Wang   +48 more
core   +1 more source

EVSS‐Based Simulation Techniques for the Viscoelastic Fluids With Pure Polymer Melts Using Three‐Field Approach

International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 492-509, April 2026.
This paper presents a finite element method for simulating highly viscoelastic flows of pure polymer melts using the Elastic Viscous Stress Splitting formulation. The method avoids higher‐order derivatives in the weak formulation by reformulating the convective term in the constitutive equation.
R. Ahmad, P. Zajac, S. Turek
wiley   +1 more source