Reconstructed Discontinuous Galerkin Methods for Diffusion Using a First-Order Hyperbolic System Formulation

2017 ◽  
Author(s):  
Jialin Lou ◽  
Xiaodong Liu ◽  
Hong Luo ◽  
Hiroaki Nishikawa
Keyword(s):  
Discontinuous Galerkin ◽  
Hyperbolic System ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
First Order

scholarly journals Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Robert Klöfkorn
Keyword(s):  
Partial Differential Equations ◽  
Discontinuous Galerkin ◽  
User Interfaces ◽  
Discontinuous Galerkin Methods ◽  
Evolution Equations ◽  
Nonlinear Partial Differential Equations ◽  
Galerkin Methods ◽  
First Order ◽  
Wide Range ◽  
Dg Method

AbstractThis paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efficient implementations of the discontinuous Galerkin (DG) method for solving a wide range of nonlinear partial differential equations (PDEs). Although the C++ interfaces of Dune-Fem-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work, easier user interfaces based on Python and the unified form language are provided to open Dune-Fem-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first-order hyperbolic PDEs.

Penalty-free discontinuous Galerkin methods for incompressible Navier–Stokes equations

2014 ◽  
Vol 24 (06) ◽  
pp. 1217-1236 ◽  
Author(s):  
Beatrice Riviere ◽  
Shirin Sardar
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Galerkin Methods ◽  
Navier Stokes Equations ◽  
First Order ◽  
Priori Error Estimates ◽  
The Stability

A first-order discontinuous Galerkin method is proposed for solving the steady-state incompressible Navier–Stokes equations. The stability of this penalty-free method is obtained by locally enriching the discrete space with a quadratic polynomial. A priori error estimates are derived. Numerical examples confirm the theoretical convergence.

Sign in / Sign up

Export Citation Format

Share Document