Uniform Convergence of the LDG Method for a Singularly Perturbed Problem with the Exponential Boundary Layer
Document Type
Article
Publication Date
3-1-2014
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this paper, we study a uniform convergence property of the local discontinuous Galerkin method (LDG) for a convection-diffusion problem whose solution has exponential boundary layers. A Shishkin mesh is employed. The trail functions in the LDG method are piecewise polynomials that lies in the space Q(k), i.e., are tensor product polynomials of degree at most k in one variable, where k > 0. We identify that the error of the LDG solution in a DG-norm converges at a rate of (ln N/N)(k+1/2); here the total number of mesh points is O(N-2). The numerical experiments show that this rate of convergence is sharp.
Publication Title
Mathematics of Computation
Volume
83
Issue
286
First Page
635
Last Page
663
Recommended Citation
Zhu, H.,
Zhang, Z.
(2014). Uniform Convergence of the LDG Method for a Singularly Perturbed Problem with the Exponential Boundary Layer. Mathematics of Computation, 83(286), 635-663.
Available at: https://aquila.usm.edu/fac_pubs/7955