A quantitative discrete H2-regularity estimate for the Shortley-Weller scheme in convex domains
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We investigate the discreteH2-regularity properties of the Shortley-Weller discretization of Poisson's equation (with homogeneous Dirichlet boundary condition) in bounded convex domains Ω⊂ℝ2. It is shown that the regularity constant is 1 independent of the mesh sizeh if theH2-seminorm is defined in a way assigning less weight to the (unsymmetric) differences near the boundary.
Subject ClassificationsAMS(MOS): 65N99 CR: G1.8
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