Convergence analysis of the LDG method applied to singularly perturbed problems. Issue 2 (30th March 2012)

• Record Type: Journal Article
• Authors: Zhu, Huiqing; Zhang, Zhimin
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 2(2013:Mar.)
• Page Start: 396
• Page End: 421
• Publication Date: 2012-03-30
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21711
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>Considering a two‐dimensional singularly perturbed convection–diffusion problem with exponential boundary layers, we analyze the local discontinuous Galerkin (DG) method that uses piecewise bilinear polynomials on Shishkin mesh. A convergence rate <italic>O</italic>(<italic>N</italic>^‐1 ln<italic>N</italic>) in a DG‐norm is established under the regularity assumptions, while the total number of mesh points is <italic>O</italic>(<italic>N</italic>²). The rate of convergence is uniformly valid with respect to the singular perturbation parameter <italic>ε</italic>. Numerical experiments indicate that the theoretical error estimate is sharp. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013</p> </abstract>