Discontinuous Galerkin Methods for Friedrichs’ Systems

Alexandre Ern () and Jean-Luc Guermond ()
Additional contact information
Alexandre Ern: Ecole nationale des ponts et chaussées, CERMICS
Jean-Luc Guermond: Dept. Math, Texas A&M

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 79-96 from Springer

Abstract: Abstract This work presents a unified analysis of Discontinuous Galerkin methods to approximate Friedrichs’ systems. A general set of boundary conditions is identified to guarantee existence and uniqueness of solutions to these systems. A formulation enforcing the boundary conditions weakly is proposed. This formulation is the starting point for the construction of Discontinuous Galerkin methods formulated in terms of boundary operators and of interface operators that mildly penalize interface jumps. A general convergence analysis is presented. The setting is subsequently specialized to two-field Friedrichs’ systems endowed with a particular 2×2 structure in which some of the unknowns can be eliminated to yield a system of second-order elliptic-like PDE’s for the remaining unknowns. A general Discontinuous Galerkin method where the above elimination can be performed in each mesh cell is proposed and analyzed. Finally, details are given for four examples, namely advection-reaction equations, advection-diffusion-reaction equations, the linear elasticity equations in the mixed stress-pressure-displacement form, and the Maxwell equations in the so-called elliptic regime.

Keywords: Boundary Operator; Discontinuous Galerkin; Discontinuous Galerkin Method; Homogeneous Dirichlet Boundary Condition; Interface Operator (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_5

Ordering information: This item can be ordered from
http://www.springer.com/9783540342885

DOI: 10.1007/978-3-540-34288-5_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().