Semidiscrete finite element Galerkin approximations to the equations of motion arising in the Oldroyd model |
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Authors: | Pani, Amiya K. Yuan, Jin Yun |
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Affiliation: | 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 |
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Abstract: | In this paper, a semidiscrete finite element Galerkin methodfor the equations of motion arising in the 2D Oldroyd modelof viscoelastic fluids with zero forcing function is analysed.Some new a priori bounds for the exact solutions are derivedunder realistically assumed conditions on the data. Moreover,the long-time behaviour of the solution is established. By introducinga StokesVolterra projection, optimal error bounds forthe velocity in the L(L2) as well as in the L(H1)-norms andfor the pressure in the L(L2)-norm are derived which are validuniformly in time t > 0. |
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