# LOCAL ERROR ESTIMATES OF THE LDG METHOD FOR 1-D SINGULARLY PERTURBED PROBLEMS

@article{Zhu2013LOCALEE, title={LOCAL ERROR ESTIMATES OF THE LDG METHOD FOR 1-D SINGULARLY PERTURBED PROBLEMS}, author={Huiqing Zhu and Zhimin Zhang}, journal={International Journal of Numerical Analysis and Modeling}, year={2013}, volume={10}, pages={350-373} }

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(hln(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… Expand

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