Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems
In this paper local discontinuous Galerkin method (LDG) was analyzed for solving 1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error estimates are established on quasi-uniform meshes with maximum mesh size h. On a subdomain with O (h ln(1/h)) distance away from the outflow boundary, the L-2 error of the approximations to the solution and its derivative converges at the optimal rate O (h(k+1)) when polynomials of degree at most k are used. Numerical experiments illustrate that the rate of convergence is uniformly valid and sharp. The numerical comparison of the LDG method and the streamline-diffusion finite element method are also presented.
International Journal of Numerican Analysis and Modeling
(2013). Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems. International Journal of Numerican Analysis and Modeling, 10(2), 350-373.
Available at: https://aquila.usm.edu/fac_pubs/7730