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Finite Difference Scheme for Filtration and Consolidation Problems
2003It's well known that numerical instabilities appear in the approximation of the Biot's consolidation problem, when standard finite elements or difference methods are applied. To stabilizate this problem, we propose the use of staggered grids for the discretization. A monotone and second order finite difference scheme on this kind of grid is given.
Francisco José Gaspar +2 more
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General derivative approximations for finite different schemes
International Journal for Numerical Methods in Engineering, 1983AbstractA general expression for finite difference approximations for all derivatives up to the (N − 1)th order on a finite difference mesh with N‐nodes is established. The mesh may be non‐uniform and the derivative evaluated at any of the N‐nodes. An estimate for the truncation error is obtained and shown to depend on the nonlinearity of the mesh as ...
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A conservative and stable explicit finite difference scheme for the diffusion equation
Journal of Computational Science, 2021Chaeyoung Lee +2 more
exaly
On the Resolution Requirements of Finite‐Difference Schemes
Studies in Applied Mathematics, 1971openaire +1 more source
An upwind finite difference scheme for meshless solvers
Journal of Computational Physics, 2003exaly