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In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12609.html} }In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.