Vol. 5, No. 1, 2012

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Multiscale adaptively weighted least squares finite element methods for convection-dominated PDEs

Bridget Kraynik, Yifei Sun and Chad R. Westphal

Vol. 5 (2012), No. 1, 39–49
Abstract

We consider a weighted least squares finite element approach to solving convection-dominated elliptic partial differential equations, which are difficult to approximate numerically due to the formation of boundary layers. The new approach uses adaptive mesh refinement in conjunction with an iterative process that adaptively adjusts the least squares functional norm. Numerical results show improved convergence of our strategy over a standard nonweighted approach. We also apply our strategy to the steady Navier–Stokes equations.

Keywords
partial differential equations, finite element methods, convection, boundary layers
Mathematical Subject Classification 2010
Primary: 65N30, 65N50, 35J57
Milestones
Received: 20 December 2010
Accepted: 4 September 2011
Published: 28 April 2012

Communicated by John Baxley
Authors
Bridget Kraynik
Department of Mathematics and Computer Science
College of Wooster
Wooster, OH 44691
United States
Yifei Sun
Department of Mathematics and Computer Science
Wabash College
Crawfordsville, IN 47933
United States
Chad R. Westphal
Department of Mathematics and Computer Science
Wabash College
Crawfordsville, IN 47933
United States