DG Method for Stokes Problem with Variable Viscosity

Stefania Lo Forte

Abstract


We study the stationary Stokes problem with varying viscosity in
. We propose and analyze a discontinuous Galerkin
method on a 1-irregular, shape-regular triangulation. We prove
the continuity of the elliptic term in the finite element space.
However, due to the presence of non constant coefficients, we
are not able to show the continuity in . Thus, we have to
resort to new techniques to show convergence. We prove that error
bounds can be derived using the continuity of the elliptic form in
the finite element space and in the piecewise space.
The error estimates are obtained with a mesh dependent norm
for the velocity and an norm for the pressure.

[DOI: 10.1685 / CSC06104]

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DOI: http://dx.doi.org/10.1685/




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