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An analysis of the cell vertex method
K W Morton,
M J Stynes
We present
a new analysis of the cell vertex finite volume method, based on the
construction of a mapping from the trial space to the test space of the
method. For a convection-diffusion problem in one dimension, we
obtain an error estimate for our computed solution (in a weighted
discrete H¹ norm) which depends only on the gradient nodal
interpolation errors. For pure convection in two dimensions, we use a
new natural seminorm to prove local and global error estimates for the
cases of flow transverse to the grid and flow parallel to the
grid.
- Subject classifications:
- AMS(MOS): 65N06, 65N12, 65N15, 65N30
- Key words and phrases:
- Finite volume, cell vertex, convection, convection-diffusion,
error estimate.
The work reported here forms part of the research programme of the
Oxford-Reading
Institute for Computational Fluid Dynamics.
This paper is not currently available electronically.
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