scholarly journals Third order positivity-preserving direct discontinuous Galerkin method with interface correction for chemotaxis Keller-Segel equations

2021 ◽  
Vol 433 ◽  
pp. 110191
Author(s):  
Changxin Qiu ◽  
Qingyuan Liu ◽  
Jue Yan
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Third Order ◽  
Positivity Preserving

scholarly journals A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

2011 ◽  
Vol 9 (2) ◽  
pp. 240-268 ◽  
Author(s):  
John Loverich ◽  
Ammar Hakim ◽  
Uri Shumlak
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Solutions ◽  
Three Dimensions ◽  
Third Order ◽  
Small Gauge ◽  
Electron Acoustic ◽  
Two Fluid ◽  
Two Fluid Plasma

AbstractA discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock [1] and existing numerical solutions to the GEM challenge magnetic reconnection problem [2]. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

2012 ◽  
Vol 12 (5) ◽  
pp. 1495-1519 ◽  
Author(s):  
Hong Luo ◽  
Luqing Luo ◽  
Robert Nourgaliev
Keyword(s):  
Galerkin Method ◽  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Least Squares Method ◽  
Polynomial Solution ◽  
Third Order ◽  
Von Neumann ◽  
Flow Problems ◽  
Dg Method

AbstractA reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.

Sign in / Sign up

Export Citation Format

Share Document