Interpolation linéaire et équations fonctionnelles
Interpolation of non-smooth functions on anisotropic finite element meshes
Interpolation of non-smooth functions on anisotropic finite element meshes
In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.
Interpolation operators on the space of holomorphic functions on the unit circle
The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval , , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...
Interpolation with prescribed values of derivatives instead of function values
Interpolation with restrictions -- role of the boundary conditions and individual restrictions
The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative...
Konstruktion und algebraische Eigenschaften von M-Spline-Interpolierenden.
-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes
An -estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space.
Linear abhängige Punktfunktionale bei zweidimensionalen Interpolations- und Approximationsproblemen.
Local interpolation by a quadratic Lagrange finite element in 1D
We analyse the error of interpolation of functions from the space in the nodes of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes change as the length of interval approaches zero.
Local representations of quartic splines
Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
Mean square approximation by optimal periodic interpolation
Following the research of Babuška and Práger, the author studies the approximation power of periodic interpolation in the mean square norm thus extending his own former results.
Mehrdimensionale Hermite-Interpolation und numerische Integration.
Mesh-based interpolation on 2-manifolds.
Meshless Polyharmonic Div-Curl Reconstruction
In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields from scattered data, possibly, contaminated by noise. We give an explicit solution of the problem. After some theoretical framework, we discuss some numerical aspect arising in the problems related to the reconstruction of vector fields
Mixed Finite Elements in IR3 .
Modified Specht's plate bending element and its convergence analysis.
Multiple root finder algorithm for Legendre and Chebyshev polynomials via Newton's method.
Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.