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BIT Numerical Mathematics

, Volume 52, Issue 4, pp 905–932 | Cite as

Stable finite difference schemes for the magnetic induction equation with Hall effect

  • Paolo Corti
  • Siddhartha Mishra
Article
  • 216 Downloads

Abstract

We consider a sub-model of the Hall-MHD equations: the so-called magnetic induction equations with Hall effect. These equations are non-linear and include third-order spatial and spatio-temporal mixed derivatives. We show that the energy of the solutions is bounded and design finite difference schemes that preserve the energy bounds for the continuous problem. We design both divergence preserving schemes and schemes with bounded divergence. We present a set of numerical experiments that demonstrate the robustness of the proposed schemes.

Keywords

Finite difference methods Stability and convergence of numerical methods 

Mathematics Subject Classification

65M06 65M12 

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Copyright information

© Springer Science + Business Media B.V. 2012

Authors and Affiliations

  1. 1.Seminar For Applied Mathematics (SAM)ETH ZentrumZürichSwitzerland

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