On stability of numerical schemes via frozen coefficients and the magnetic induction equations

On stability of numerical schemes via frozen coefficients and the magnetic induction equations: "

Abstract We study finite difference discretizations of initial boundary value problems for linear symmetric hyperbolic systems of equations
in multiple space dimensions. The goal is to prove stability for SBP-SAT (Summation by Parts—Simultaneous Approximation Term)
finite difference schemes for equations with variable coefficients. We show stability by providing a proof for the principle
of frozen coefficients, i.e., showing that variable coefficient discretization is stable provided that all corresponding constant
coefficient discretizations are stable.

We apply this general result to the special case of magnetic induction equations and show that high order SBP-SAT schemes
are energy stable even with boundary closures. Furthermore, we introduce a modified discretization of lower order terms and
show that the discrete divergence of this scheme is bounded. The discrete divergence is shown to converge to zero under certain
assumptions. Computations supporting our theoretical results are also presented.

• Content Type Journal Article
• DOI 10.1007/s10543-010-0249-5
• Authors
  
  
  • Siddhartha Mishra, University of Oslo Centre of Mathematics for Applications P.B. 1053 Blindern 0316 Oslo Norway
  • Magnus Svärd, University of Oslo Centre of Mathematics for Applications P.B. 1053 Blindern 0316 Oslo Norway
  
  

• Journal BIT Numerical Mathematics
• Online ISSN 1572-9125
• Print ISSN 0006-3835

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