IMA Journal of Numerical Analysis · 1987 · 16 citations · 0 references
ComputingComputational EngineeringComputational GeometryFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Difference MethodsNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical StabilityConvergenceElliptic Equation SchemesElliptic Partial Differential EquationsFinite Difference DiscretizationFinite Difference Schemes
We study the convergence of finite-difference schemes for second-order elliptic equations with variable coefficients. We prove that the convergence rate in the discrete W21 norm is of the order hs −1 if the solution of the boundary value problem belongs to the Sobolev space W2s (1 < s ≤ 3).