Quadratic convergence for cell-centered grids
Rectangular cell-centered finite difference approximations of a plane pressure-flow equation in a rectangular region with no-flow conditions at the boundary are considered. Despite a formal inconsistency in the finite difference equations, due to the use of cell-centered rather than point- distributed grids, it is shown that the solution errors are \(O(h^ 2)\) when the mesh width \(h\to 0\). The methods are quite elementary and rely upon an explicit treatment of truncation error terms which are not \(O(h^ 2)\).
scientific article; zbMATH DE number 4062527