5,925 research outputs found
A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension
Finite volume methods for problems involving second order operators with full
diffusion matrix can be used thanks to the definition of a discrete gradient
for piecewise constant functions on unstructured meshes satisfying an
orthogonality condition. This discrete gradient is shown to satisfy a strong
convergence property on the interpolation of regular functions, and a weak one
on functions bounded for a discrete norm. To highlight the importance of
both properties, the convergence of the finite volume scheme on a homogeneous
Dirichlet problem with full diffusion matrix is proven, and an error estimate
is provided. Numerical tests show the actual accuracy of the method
Superconvergence Using Pointwise Interpolation in Convection-Diffusion Problems
Considering a singularly perturbed convection-diffusion problem, we present
an analysis for a superconvergence result using pointwise interpolation of
Gau{\ss}-Lobatto type for higher-order streamline diffusion FEM.
We show a useful connection between two different types of interpolation,
namely a vertex-edge-cell interpolant and a pointwise interpolant. Moreover,
different postprocessing operators are analysed and applied to model problems.Comment: 19 page
VAGO method for the solution of elliptic second-order boundary value problems
Mathematical physics problems are often formulated using differential
oprators of vector analysis - invariant operators of first order, namely,
divergence, gradient and rotor operators. In approximate solution of such
problems it is natural to employ similar operator formulations for grid
problems, too. The VAGO (Vector Analysis Grid Operators) method is based on
such a methodology. In this paper the vector analysis difference operators are
constructed using the Delaunay triangulation and the Voronoi diagrams. Further
the VAGO method is used to solve approximately boundary value problems for the
general elliptic equation of second order. In the convection-diffusion-reaction
equation the diffusion coefficient is a symmetric tensor of second order
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