Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
Copyright policy )Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
Summary: Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over \(h^2\)-uniform quadrilateral meshes. The superconvergence holds for a full tensor coefficient. The analysis exploits a relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar product in the velocity space. The theoretical results are confirmed by numerical experiments.
- Los Alamos National Laboratory United States
- University of Pittsburgh United States
Flows in porous media; filtration; seepage, quadrature rule, mixed finite element, tensor coefficient, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite difference methods applied to problems in fluid mechanics, Finite element methods applied to problems in fluid mechanics
Flows in porous media; filtration; seepage, quadrature rule, mixed finite element, tensor coefficient, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite difference methods applied to problems in fluid mechanics, Finite element methods applied to problems in fluid mechanics
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