Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Convergence Characteristics of the Crank-Nicolson-Galerkin Scheme for Linear Parabolic Systems

  • Cho, Jin-Rae (Research Institute of Mechanical Technology,Pusan National University) ;
  • Ha, Dae-Yul (Research Institute of Mechanical Technology,Pusan National University) ;
  • Kim, Tae-Jong (Research Institute of Mechanical Technology,Pusan National University)
  • Published : 2002.10.01
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Abstract

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

Keywords

References

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