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The $\ell_2-$ and $\ell_1-$regularized modified Lagrange interpolation formulae over $[-1,1]$ are deduced in this paper. This paper mainly analyzes the numerical characteristics of regularized barycentric interpolation formulae, which are…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

This paper presents the symmetric wave interpolation method for stable global interpolation using readily available equidistant points. Its key achievement is the integration of the practical utility of such points with the numerical…

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…

We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in…

Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…

Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…

This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…

This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…

In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without polynomial addition.

Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…

This paper is addressed to a stabilization problem of a system coupled by a wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be damped. Under some assumption about the damping and the coupling terms, it is shown…

We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…

Semi-implicit semi-Lagrangian (SISL) methods are commonly used for the shallow water equations (SWE) because they allow for larger time steps than those permitted by the Courant-Friedrichs-Lewy (CFL) stability condition in Eulerian schemes.…

We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…

We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…

The direct method used for calculating smooth radial basis function (RBF) interpolants in the flat limit becomes numerically unstable. The RBF-QR algorithm bypasses this ill-conditioning using a clever change of basis technique. We extend…

A major obstacle to the application of the standard Radial Basis Function-generated Finite Difference (RBF-FD) meshless method is constituted by its inability to accurately and consistently solve boundary value problems involving Neumann…

We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in $\mathbb{R}^n$. We consider the normal derivative volume stabilization and add an…

Image resizing is a basic tool in image processing and in literature we have many methods, based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or…