J. E. Castillo

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K e y w o r d s T i m e scales, Measure chains, Mimetic propert ies, Divergence, Gradient , Laplacian. 1. I N T R O D U C T I O N Mimet ic discretizations of differential operators are discretizations that preserve many of the fundamental properties of the continuum differential operators. Certainly any reasonable discretization will preserve some of the(More)
In this work we perform an experimental study of iterative methods for solving large sparse linear systems arising from a second-order 2D mimetic discretization. The model problem is the 2D Poisson equation with different boundary conditions. We use GMRES with the restarted parameter and BiCGstab as iterative methods. We also use various preconditioning(More)
By combining the support-operators method with the mapping method, we have derived new mimetic fourthorder accurate discretizations of the divergence, gradient, and Laplacian on nonuniform grids. These finite difference operators mimic the differential and integral identities satisfied by the differential operators. For example, the discrete divergence is(More)
J. M. Guevara-Jordan (jguevara@euler.ciens.ucv.ve) Departamento de Matemáticas, Universidad Central de Venezuela S. Rojas (srojas@usb.ve) Departamento de F́ısica, Universidad Simón Boĺıvar M. Freites-Villegas (mayrafreites@cantv.net) Departamento de Estad́ıstica Computacional, Universidad Simón Boĺıvar J. E. Castillo (castillo@myth.sdsu.edu) Computational(More)
The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integral identities is more likely to produce better approximations. Recently, one of the authors developed a systematic approach to obtain mimetic finite(More)
Variational grid generation techniques are now used to produce grids suitable for solving numerical partial differential equations in irregular geometries. Variational grid generation methods are very robust but slow. The method considered here is a discrete variational method. This method preserves the robustness of the variational method; also, it is very(More)
We derive conservative fourthand sixth-order finite difference approximations for the divergence and gradient operators and a compatible inner product on staggered 1D uniform grids in a bounded domain. The methods combine standard centered difference formulas in the interior with new one-sided finite difference approximations near the boundaries. We derive(More)
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