#### Title

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