MATH 590: Meshfree Methods - Chapter 6 - Applied Mathematics

Interpolation with Multivariate PolynomialsRemarkLater on we will be interested in applying our interpolation methods tothe numerical solution of partial differential equations, and practitioners(especially of finite element methods) often judge an interpolationmethod by its ability to pass the so-called patch test.An interpolation method passes the standard patch test if it canreproduce linear functions. In engineering applications this translatesinto exact calculation of constant stress and strain.We will see later that in order to prove error estimates for meshfreeapproximation methods it is not necessary to be able to reproducepolynomials globally (but local polynomial reproduction is an essentialingredient).Thus, if we are only concerned with the approximation power of anumerical method there is really no need for the standard patch test tohold.fasshauer@iit.edu MATH 590 – Chapter 6 13