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105
Se considera la interpolación de Hermite de funciones de una variable mediante polinomios generalizados. Se pretende mostrar que técnicas computacionales conocidas para interpolación polinómica se pueden aplicar también a interpolación mediante polinomios generalizados. Como aplicación se estudia con cierto detalle la interpolación mediante funciones racionales con polos prefijados. La interpolación polinómica corresponde al caso particular en que todos los polos prefijados están en el infinito.
Hermite polynomial interpolation is investigated.
Some approximation results are obtained. As an example, the Burgers
equation on the whole line is considered. The stability and the
convergence of proposed Hermite pseudospectral scheme are proved
strictly. Numerical results are presented.
This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle-In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being...
We study the approximation properties of some finite element subspaces of H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div;Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of vector fields on the reference cube, which is then transformed to a space of vector fields on a hexahedron using...
We study the approximation properties of some finite element subspaces of
H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This
work extends results previously obtained for quadrilateral H(div;Ω) finite
elements and for quadrilateral scalar finite element spaces. The finite
element spaces we consider are constructed starting from a given finite
dimensional space of vector fields on the reference cube, which is then
transformed to a space of vector fields on a hexahedron...
In the present work the symmetrized sequential-parallel decomposition method of the third degree precision for the solution of Cauchy abstract problem with an operator under a split form, is presented. The third degree precision is reached by introducing a complex coefficient with the positive real part. For the considered schema the explicit a priori estimation is obtained.
In the present work the symmetrized sequential-parallel decomposition method
of the third degree precision for the solution of Cauchy abstract problem
with an operator under a split form, is presented. The third degree
precision is reached by introducing a complex coefficient with the positive
real part. For the considered schema the explicit a priori estimation is
obtained.
We analyze the regularity of random entropy solutions to scalar hyperbolic conservation laws with random initial data. We prove regularity theorems for statistics of random entropy solutions like expectation, variance, space-time correlation functions and polynomial moments such as gPC coefficients. We show how regularity of such moments (statistical and polynomial chaos) of random entropy solutions depends on the regularity of the distribution law of the random shock location of the initial data....
Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex.
In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one.
We give a geometrical localization of all degrees of freedom over particular edges and provide
a basis for these elements on simplicial meshes.
As for Whitney edge elements of degree one, the basis is...
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105