A quantitative discrete \(H^ 2\)-regularity estimate for the Shortley- Weller scheme in convex domains (Q1099934)

The paper is concerned with the discrete \(H^ 2\)-regularity properties of the Shortley-Weller discretization of Poisson's equation (with homogeneous Dirichlet boundary condition) in bounded convex domains \(\Omega \in {\mathbb{R}}^ 2\). It is shown that the regularity constant is 1 independent of the mesh size h if the \(H^ 2\)-seminorm is defined in a way assigning less weight to the (unsymmetric) differences near the boundary.