Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations
The author analyzes the multi-dimensional convection-diffusion equation with various boundary conditions using the direct discontinuous Galerkin (DDG) method. First, he presents the admissible parameter set for the DDG diffusive flux to ensure that the projection defined by the same DDG method to the elliptic problem is well-defined. Then he obtains the optimal projection error in \(L^2\). Finally, he presents \(L^2\) error estimates for the numerical solution to the nonlinear convection-diffusion with various boundary conditions.
scientific article; zbMATH DE number 7341057
scientific article