Local analysis of the local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularly perturbed problem
The authors perform the local analysis of the local discontinuous Galerkin (LDG) method based on the generalized alternating flux to solve the one-dimensional time-dependent singularly perturbed problem. The semi-discrete LDG scheme and a fully discrete scheme with explicit time marching are considered. Based on the elemental stability with a suitable weight function we can establish the local stability and local error estimate. The double-optimal local error estimate is also obtained and it is shown that the projection error has the exponential decay property. Some numerical examples are performed that indicate the existence of the double optimal local estimates implying that the results could also be extended to nonlinear cases. Some lemmas and theorems are stated and proved.
scientific article; zbMATH DE number 6805227
scientific article