Approximate Hermite quasi-interpolation
arXiv:0806.25462 citationsh-index: 46
Originality Synthesis-oriented
AI Analysis
Provides a practical tool for high-order approximation in numerical PDE solving, but the method is incremental.
The paper derives approximate quasi-interpolants using function and derivative values on a uniform grid, yielding simple high-order approximants for elliptic PDEs with constant coefficients.
In this paper we derive approximate quasi-interpolants when the values of a function $u$ and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants which provide high order approximations for solutions to elliptic differential equations with constant coefficients.