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 NUMERICAL ANALYSIS AND MODELING
(2013). LOCAL ERROR ESTIMATES OF THE LDG METHOD FOR 1-D SINGULARLY PERTURBED PROBLEMS. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 10(2), 350-373.
Available at: http://aquila.usm.edu/fac_pubs/7730