Finite element interpolation of nonsmooth functions satisfying boundary conditions

Finite Element Interpolation of Nonsmooth Functions

In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on dor (d 1 )-simplices to generate nodal values for the interpolatio...

Hermite interpolation of nonsmooth functions preserving boundary conditions

This article is devoted to the construction of a Hermite-type regularization operator transforming functions that are not necessarily C1 into globally C1 finite-element functions that are piecewise polynomials. This regularization operator is a projection, it preserves appropriate first and second order polynomial traces, and it has approximation properties of optimal order. As an illustration,...

Cover interpolation functions and h-enrichment in finite element method

This paper presents a method to improve the generation of meshes and the accuracy of numerical solutions of elasticity problems, in which two techniques of h-refinement and enrichment are used by interpolation cover functions. Initially, regions which possess desired accuracy are detected. Mesh improvment is done through h-refinement for the elements existing in those regions. Total error of th...

Interpolation functions in the immersed boundary and finite element methods

In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the ex...

Analytic Functions Satisfying Hljlder Conditions on the Boundary