Uniform Convergence of the LDG Method for a Singularly Perturbed Problem with the Exponential Boundary Layer
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.
Mathematics of Computation
(2014). Uniform Convergence of the LDG Method for a Singularly Perturbed Problem with the Exponential Boundary Layer. Mathematics of Computation, 83(286), 635-663.
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