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Error analysis of a DG method employing ideal elements applied to a nonlinear convection--diffusion problem.
- Source :
- Journal of Numerical Mathematics; 2011, Vol. 19 Issue 2, p137-163, 27p
- Publication Year :
- 2011
-
Abstract
- In this paper we use the discontinuous Galerkin finite element method for the space-semidiscretization of a nonlinear nonstationary convection--diffusion problem defined on a nonpolygonal two-dimensional domain. Using Zláámal's concept of the ideal curved elements, we define a finite element space . We prove the ''ideal'' versions of the inverse and the multiplicative trace inequalities known for standard straight triangulations. Further, we define a projection on the finite element space and study its approximation properties. The obtained results allow us to derive an H<superscript>1</superscript>-optimal error estimate for the discontinuous Galerkin method employing the ideal curved elements. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15702820
- Volume :
- 19
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 62665895
- Full Text :
- https://doi.org/10.1515/JNUM.2011.007