Abstract and Applied Analysis · 2012 · 17 citations · 8 references
Natural SciencesComputational EngineeringPhysicsComputational MechanicsDifferential EquationsFinite Element MethodsBoundary ConditionsBoundary-value ProblemsFinite Difference MethodsNumerical Methods For Differential EquationsNumerical StabilityPartial Differential EquationsBoundary Value Problem SolversCoercivityElliptic Boundary-value ProblemsElliptic Partial Differential EquationsFinite Difference SchemesNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsStability Of Finite Difference Schemes
A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze‐Samarskii‐Dirichlet condition. The first and second‐orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.
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