H-1 least-squares method for the velocity-pressure-stress formulation of Stokes equations

Authors:
Sang Dong Kim;Byeong Chun Shin
Affiliations:
Department of Mathematics, Kyungpook National University, Taegu, Republic of Korea;Department of Mathematics, Seoul National University, Seoul, Republic of Korea
Venue:
Applied Numerical Mathematics
Year:
2002

Citing 9
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Abstract

This paper studies the discrete H-1-norm least-squares method for the incompressible Stokes equations based on the velocity-pressure-stress formulation by the least-squares functional defined as the sum of L2-norms and H-1-norm of the residual equations. Some computational experiments by multigrid method and preconditioning conjugate gradient method (PCGM) on this method are shown by taking efficient α and β in the discrete solution operator Th = αh2I + βBh corresponding to the minus one norm. We also propose a new method and compare it with PCGM and multigrid method through the analysis of numerical experiments depending on the choice of β.