A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

Abstract

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Keywords:

• Boundary element method
• Cauchy problem
• Conjugate gradient
• Inverse problem
• Regularization
• Stokes flow

Keywords:

• AMS Subject Classifications:
• 35R25
• 47A52
• 76D07

Acknowledgements

The first author acknowledges grants and support from the Wenner-Gren foundations. Both authors would like to thank the referee for constructive suggestions.