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IMA Journal of Numerical Analysis Advance Access originally published online on August 25, 2005
IMA Journal of Numerical Analysis 2005 25(4):750-782; doi:10.1093/imanum/dri016
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Semidiscrete finite element Galerkin approximations to the equations of motion arising in the Oldroyd model

Amiya K. Pani1 and Jin Yun Yuan2

1 Industrial Mathematics Group, Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, India, 2 Department of Mathematics, Federal University of Paraná, Curitiba, Centro Politécnico, Cx.P: 19081, CEP: 81531-990, PR, Brazil

In this paper, a semidiscrete finite element Galerkin method for the equations of motion arising in the 2D Oldroyd model of viscoelastic fluids with zero forcing function is analysed. Some new a priori bounds for the exact solutions are derived under realistically assumed conditions on the data. Moreover, the long-time behaviour of the solution is established. By introducing a Stokes–Volterra projection, optimal error bounds for the velocity in the L{infty}(L2) as well as in the L{infty}(H1)-norms and for the pressure in the L{infty}(L2)-norm are derived which are valid uniformly in time t > 0.


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