Inf–sup testing of upwind methods

✍ Scribed by Klaus-Jürgen Bathe; Dena Hendriana; Franco Brezzi; Giancarlo Sangalli

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 130 KB
• Volume: 48
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(20000620)48:5<745::aid-nme904>3.0.co;2-e

✦ Synopsis

We propose inf-sup testing for ÿnite element methods with upwinding used to solve convection-di usion problems. The testing evaluates the stability of a method and compactly displays the numerical behaviour as the convection e ects increase. Four discretization schemes are considered: the standard Galerkin procedure, the full upwind method, the Galerkin least-squares scheme and a high-order derivative artiÿcial di usion method. The study shows that, as expected, the standard Galerkin method does not pass the inf-sup tests, whereas the other three methods pass the tests. Of these methods, the high-order derivative artiÿcial di usion procedure introduces the least amount of artiÿcial di usion.