A local projection stabilization for convection-diffusion-reaction equations using biorthogonal systems

Bishnu P. Lamichhane; Jordan A. Shaw-Carmody

doi:10.21914/anziamj.v64.17543

Authors

Bishnu P. Lamichhane University of Newcastle https://orcid.org/0000-0002-9184-8941
Jordan University of Newcastle https://orcid.org/0000-0002-6034-4644

DOI:

https://doi.org/10.21914/anziamj.v64.17543

Keywords:

advection-dominated problem, biorthogonal system, local projection stabilization

Abstract

We consider a local projection stabilization based on biorthogonal systems for convection–diffusion–reaction differential equations with mixed boundary conditions. The approach based on biorthogonal systems is numerically more efficient than other existing approaches to obtain a uniform approximation for convection dominated problems. We prove optimal a priori error estimates for the proposed numerical technique. Numerical examples are presented to demonstrate the performance of the approach.

doi: 10.1017/S1446181123000019

Author Biographies

Bishnu P. Lamichhane, University of Newcastle

School of Information and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia.

Jordan, University of Newcastle