Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii

Abstract  We prove the existence of weak solutions to the harmonic map heat flow, and wave maps into spheres of nonconstant radii. Weak
solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite
elements, where discrete Lagrange multipliers are employed to exactly meet the sphere constraint at mesh-points. Computational
studies are included to motivate interesting dynamics in two and three spatial dimensions.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0282-y
• Authors
  
  
  • L’ubomír Baňas, Heriot-Watt University Department of Mathematics and the Maxwell Institute for Mathematical Sciences Edinburgh EH14 4AS UK
  • Andreas Prohl, Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen Germany
  • Reiner Schätzle, Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen Germany
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

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Original source : http://www.springerlink.com/content/22g15824q3016g...

MIT Researchers Simulate New Materials on Ranger to Improve Solar Photovoltaic Cells

To better understand the fundamentals of solar energy conversion and to identify potential new materials for cheaper and more efficient cells, researchers from MIT have been simulating the atomic behavior of solar cells using the Ranger supercomputer at TACC.

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Original source : http://www.hpcwire.com/industry/academia/MIT-Resea...

Curved Boundary Treatments for the Discontinuous Galerkin Method Applied to Aeroacoustic Propagation

AIAA Journal Feb. 2010, Vol. 48: 479-489.

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Original source : http://doi.aiaa.org/10.2514/1.45353...

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AIAA Journal Feb. 2010, Vol. 48: 354-371.

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Original source : http://doi.aiaa.org/10.2514/1.43753...

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Pseudopotential for ground state hydrogen molecule with nonadiabatic corrections

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Further results on error estimators for local refinement with first-order system least squares (FOSLS)

Adaptive local refinement (ALR) can substantially improve the performance of simulations that involve numerical solution of partial differential equations. In fact, local refinement capabilities are one of the attributes of first-order system least squares (FOSLS) in that it provides an inexpensive but effective a posteriori local error bound that accurately identifies regions that require further refinement. Previous theory on FOSLS established the effectiveness of its local error estimator, but only under the assumption that the local region is not too 'thin'. This paper extends this theory to the case of a rectangular domain by showing that the estimator's effectiveness holds even for certain 'thin' local regions. Further, we prove that when the approximation satisfies a local saturation property, convergence of a FOSLS ALR scheme is guaranteed. Copyright © 2010 John Wiley & Sons, Ltd.

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Original source : http://dx.doi.org/10.1002%2Fnla.696...