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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 65N30, 65N50, 35J57
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Milestones
Received: 20 December 2010
Accepted: 4 September 2011
Published: 28 April 2012
Communicated by John Baxley
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Authors |
| Bridget Kraynik | |
| Department of Mathematics and
Computer Science College of Wooster Wooster, OH 44691 United States |
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| Yifei Sun | |
| Department of Mathematics and
Computer Science Wabash College Crawfordsville, IN 47933 United States |
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| Chad R. Westphal | |
| Department of Mathematics and
Computer Science Wabash College Crawfordsville, IN 47933 United States |
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