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Improving Conservation for First-Order System Least-Squares Finite-Element Methods

  • J. H. Adler
  • P. S. VassilevskiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 45)

Abstract

The first-order system least-squares (FOSLS) finite element method for solving partial differential equations has many advantages, including the construction of symmetric positive definite algebraic linear systems that can be solved efficiently with multilevel iterative solvers. However, one drawback of the method is the potential lack of conservation of certain properties. One such property is conservation of mass. This paper describes a strategy for achieving mass conservation for a FOSLS system by changing the minimization process to that of a constrained minimization problem. If the space of corresponding Lagrange multipliers contains the piecewise constants, then local mass conservation is achieved similarly to the standard mixed finite-element method. To make the strategy more robust and not add too much computational overhead to solving the resulting saddle-point system, an overlapping Schwarz process is used.

Keywords

Conservation First-order system least-squares Finite elements Domain decomposition Two-level 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA
  2. 2.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA

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