Convergence Analysis of the LDG Method Applied to Singularly Perturbed Problems
Document Type
Article
Publication Date
3-1-2013
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
Considering a two-dimensional singularly perturbed convectiondiffusion problem with exponential boundary layers, we analyze the local discontinuous Galerkin (DG) method that uses piecewise bilinear polynomials on Shishkin mesh. A convergence rate O(N-1 lnN) in a DG-norm is established under the regularity assumptions, while the total number of mesh points is O(N2). The rate of convergence is uniformly valid with respect to the singular perturbation parameter epsilon. Numerical experiments indicate that the theoretical error estimate is sharp. (C) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013
Publication Title
Numerical Methods for Partial Differential Equations
Volume
29
Issue
2
First Page
396
Last Page
421
Recommended Citation
Zhu, H.,
Zhang, Z.
(2013). Convergence Analysis of the LDG Method Applied to Singularly Perturbed Problems. Numerical Methods for Partial Differential Equations, 29(2), 396-421.
Available at: https://aquila.usm.edu/fac_pubs/7654