On ε-Uniform Error Estimates For Singularly Perturbed Problems in the DG Method

V. Kučera ()
Additional contact information
V. Kučera: Charles University, Faculty of Mathematics and Physics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 369-378 from Springer

Abstract: Abstract In this paper we present the analysis of the discontinuous Galerkin (DG) finite element method applied to a nonstationary nonlinear convection-diffusion problem. Using the technique of Zhang and Shu (SIAM J Numer Anal 42(2):641–666, 2004), originally for explicit schemes, we prove apriori error estimates uniform with respect to the diffusion coefficient and valid even in the purely convective case. We extend the cited analysis to the method of lines using continuous mathematical induction and a nonlinear Gronwall-type lemma. For an implicit scheme, we prove that there does not exist a Gronwall-type lemma capable of proving the desired estimates using standard arguments. Next, we use a suitable continuation of the implicit solution and use continuous mathematical induction to prove error estimates under a CFL-like condition.

Keywords: Discontinuous Galerkin; Implicit Scheme; Numerical Flux; Gronwall Lemma; Discontinuous Galerkin Scheme (search for similar items in EconPapers)
Date: 2013
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:978-3-642-33134-3_40

Ordering information: This item can be ordered from
http://www.springer.com/9783642331343

DOI: 10.1007/978-3-642-33134-3_40

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 ().