An a posteriori error bound for discontinuous Galerkin approximations of convection–diffusion problems. (22nd December 2017)

• Record Type: Journal Article
• Authors: Georgoulis, Emmanuil H; Hall, Edward; Makridakis, Charalambos
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 1(2019)
• Page Start: 34
• Page End: 60
• Publication Date: 2017-12-22
• Subjects: convection–diffusion problems -- a posteriori error bounds' singular limit; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drx065
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: An a posteriori bound for the error measured in the discontinuous energy norm for a discontinuous Galerkin (dG) discretization of a linear one-dimensional stationary convection–diffusion–reaction problem with essential boundary conditions is presented. The proof is based on a conforming recovery operator inspired from a posteriori error bounds for the dG method for first-order hyperbolic problems. As such, the bound remains valid in the singular limit of vanishing diffusion. Detailed numerical experiments demonstrate the independence of the quality of the a posteriori bound with respect to the Péclet number in the standard dG-energy norm, as well as with respect to the viscosity parameter.