Results 11 to 20 of about 732 (184)

Quail: A lightweight open-source discontinuous Galerkin code in Python for teaching and prototyping

SoftwareX, 2022
In this paper, we present Quail, a lightweight discontinuous Galerkin solver written in Python. The aim of this code is to serve not only as a teaching tool for newcomers to the rapidly growing field, but also as a prototyping platform for testing ...
Eric J. Ching, Brett Bornhoft, Ali Lasemi, Matthias Ihme   +3 more
doaj   +1 more source

L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Journal of Inequalities and Applications, 2010
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Hyun Young Lee, Mi Ray Ohm, Jun Yong Shin   +2 more
doaj   +1 more source

ADER discontinuous Galerkin Material Point Method

International Journal for Numerical Methods in Engineering, 2023
AbstractThe first‐order accurate discontinuous Galerkin Material Point Method (DGMPM), initially introduced by Renaud et al. (J Comput Phys. 2018;369:80–102.), considers a solid body discretized by a collection of material points carrying the history of the matter, embedded in an arbitrary grid on which a nodal discontinuous Galerkin approximation is ...
Alaa Lakiss, Thomas Heuzé, Mikhael Tannous, Laurent Stainier   +3 more
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Error Estimates for Local Discontinuous Galerkin Methods for Linear Fourth-order Equations

Journal of Harbin University of Science and Technology, 2021
This paper studies the stability and error estimates of the local discontinuous Galerkin method for fourth-order linear partial differential equations based on upwind-biased fluxes. Consider using the semi-discrete form of numerical format in the spatial
BI Hui, CHEN Sha-sha
doaj   +1 more source

Comparison of the stability of discontinuous Galerkin and finite-difference methods

Lietuvos Matematikos Rinkinys, 2002
In this article we present stability analysis of two discrete schemes, which are used to solve a parabolic problem on adaptive nonstationary meshes. The influence of interpolation and projection errors is investigated.
Raimondas Čiegis, Remigijus Čiegis, Olga Suboč   +2 more
doaj   +3 more sources

Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation

Mathematical Modelling and Analysis, 2012
In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation.
Zongxiu Ren, Leilei Wei, Yinnian He, Shaoli Wang   +3 more
doaj   +1 more source

A Discontinuous Galerkin like Coarse Space correction for Domain Decomposition Methods with continuous local spaces: the DCS-DGLC Algorithm

ESAIM: Proceedings and Surveys, 2014
In this paper, we are interested in scalable Domain Decomposition Methods (DDM). To this end, we introduce and study a new Coarse Space Correction algorithm for Optimized Schwarz Methods(OSM): the DCS-DGLC algorithm.
Santugini Kévin
doaj   +1 more source

A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media

Results in Applied Mathematics, 2020
An hybridizable discontinuous Galerkin method of arbitrary high order is formulated to solve the miscible displacement problem in porous media. The spatial discretization is combined with a sequential algorithm that decouples the flow and the transport ...
Maurice S. Fabien, Matthew Knepley, Beatrice Riviere   +2 more
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Multisymplecticity of Hybridizable Discontinuous Galerkin Methods [PDF]

Foundations of Computational Mathematics, 2019
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential equations. We show that these conditions are satisfied by the "hybridized" versions of several of the most commonly-used ...
McLachlan, Robert I., Stern, Ari
openaire   +3 more sources

Robust Interior Penalty Discontinuous Galerkin Methods

Journal of Scientific Computing, 2022
Classical interior penalty discontinuous Galerkin (IPDG) methods for diffusion problems require a number of assumptions on the local variation of mesh-size, polynomial degree, and of the diffusion coefficient to determine the values of the, so-called, discontinuity-penalization parameter and/or to perform error analysis.
Dong, Zhaonan, Georgoulis, Emmanuil
openaire   +2 more sources