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Keywords:

  • Sobolev equation;
  • mixed covolume method;
  • expanded mixed covolume method;
  • Raviart-Thomas spaces;
  • optimal error estimate

Abstract

The expanded mixed covolume method for the two-dimensional Sobolev equation with convection term is developed and studied. This method uses the lowest-order Raviart-Thomas mixed finite element space as the trial function space. By introducing a transfer operator γh which maps the trial function space into the test function space and combining expanded mixed finite element with mixed covolume method, the continuous-in-time, discrete-in-time expanded mixed covolume schemes are constructed, and optimal error estimates for these schemes are obtained. Numerical results are given to examine the validity and effectiveness of the proposed schemes.© 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013