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

Authors:
R. Abgrall;J. Trefilík
Affiliations:
Team Bacchus, INRIA Bordeaux Sud Ouest & Institut de Mathéématiques de Bordeaux, Talence, France 33 405 and Institut Polytechnique de Bordeaux, Talence, France 33 405;Team Bacchus, INRIA Bordeaux Sud Ouest & Institut de Mathéématiques de Bordeaux, Talence, France 33 405 and CTU Prague, Praha 2, Czech Republic 12 135
Venue:
Journal of Scientific Computing
Year:
2010

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Abstract

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.