An Example of High Order Residual Distribution Scheme Using non-Lagrange Elements

We are interested in the numerical approximation of non-linear hyperbolic problems. The particular class of schemes we are interested in are the so-called Residual Distribution (RD) schemes. In their current form, they rely on the Lagrange interpolation of the point values of the approximated functions. This interpretation of the degrees of freedom as point values plays a fundamental role in the derivation of the schemes. The purpose of the present paper is to show that some non-Lagrange elements can also do the job, and maybe better. This opens the door to isogeometric analysis in the framework of RDS schemes.