In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are class C2 on the whole domain but fourth-order regularity is required at vertices and C3 imposed across edges refined triangulation also interior point chosen to define refinement. An algorithm proposed triangles with small area diameter needed construct no...

Recently, Kulikov presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely, a local error control implemented in doubly quasi-consistent numerical methods plays a part of global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme ...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

A quasi-interpolation method for quadratic piecewise polynomials in three variables is described which can be used for the efficient visualization of gridded volume data. We analyze the smoothness properties of the trivariate splines. We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives...

We show that a nested sequence of C macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H(Ω), 1 < s < r+ 3 2 , and H 0(Ω), 1 < s < σ+ 3 2 , s / ∈ Z+ 1 2 , as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of H 0(Ω), the nodal interpolation operators ...

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and ...

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and ...