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

Alternating evolution discontinuous Galerkin methods for convection-diffusion equations

Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations

In this work, we propose a high resolution Alternating Evolution Discontinuous Galerkin (AEDG) method to solve Hamilton-Jacobi equations. The construction of the AEDG method is based on an alternating evolution system of the Hamilton-Jacobi equation, following the previous work [H. Liu, M. Pollack and H. Saran, SIAM J. Sci. Comput. 35(1), (2013) 122–149] on AE schemes for Hamilton-Jacobi equati...

Discontinuous Galerkin Methods for Partial Differential Equations

Day 1: Monday, September 26, 2011 Hybridized DG Method and Mimetic Finite Differences Franco Brezzi IUSS and IMATI-CNR, Pavia Via Ferrata 1, 27100 Pavia [email protected] Abstract: The talk will discuss the relationships between certain variants of Mimetic Finite Differences and the Hybridized version of DG methods for some very simple model problem. The talk will discuss the relationships be...

Discontinuous Galerkin Methods for Fractional Diffusion Equations

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems, characterized by having fractional derivatives, parameterized by β ∈ [1, 2]. We show through analysis that one can construct a numerical flux which results in a scheme that exhibit optimal order of convergence O(hk+1) in the continuous range between pure advection (β = 1) and pure...

Discontinuous Galerkin Methods for Vlasov-maxwell Equations

In this paper, we propose to use discontinuous Galerkin methods to solve the Vlasov-Maxwell system. Those methods are chosen because they can be designed systematically as accurate as one wants, meanwhile with provable conservation of mass and possibly also of the total energy. Such property in general is hard to achieve within other numerical method frameworks to simulate the Vlasov-Maxwell sy...