Some algorithms for quartic smoothing splines
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some results in multivariate interpolation.
Special curved elements and theitr application [Abstract of thesis]
Spectral approach for kernel-based interpolation
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
Spherical basis function approximation with particular trend functions
The paper is concerned with the measurement of scalar physical quantities at nodes on the -dimensional unit sphere surface in the -dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider . We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful...
Spline recurrences for quartic splines
Spolehlivost numerických výpočtů
Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles
An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: are the vertices of triangles without obtuse inner angles such that has one side common with for .
Superconvergence of the gradient of finite element solutions
Sur les éléments finis rationnels de Serendip de degré quelconque.
Sur les elements finis rationnels de Wachspress.
Sur l’évaluation de l’erreur d’interpolation de Lagrange dans un ouvert de
Sur l’évaluation de l’erreur d’interpolation de Lagrange dans un ouvert de
Surface interpolation with local control by linear blending.
Tetrahedral finite -elements
The asymptotic distribution of general interpolation arrays for exponential weights.
The Bias of Least Squares Polynomial Interpolants.
The Norm of a Function with Prescribed Jets III.