Error estimates for higher-order finite volume schemes for convection-diffusion problems
The authors consider higher order schemes MUSCL type for the discretization of convection dominated elliptic problems in a convex bounded domain \(\varOmega\) in \(\mathbb{R}^{2}\). Some \textit{a priori} error estimates are proved. In the part of the estimate, which refers to the discretization of the convective term, the order is improved by \(h^{1/2}\). Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.
linear convection dominated diffusion equation in 2D
first and higher order finite volume schemes
scientific article; zbMATH DE number 6861148
scientific article