A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids

作者：Pani Amiya K^*; Pany Ambit K; Damazio Pedro; Yuan Jin Yun

来源：APPLICABLE ANALYSIS, 2014, 93(8): 1587-1610.

DOI：10.1080/00036811.2013.841143

• viscoelastic fluids
• Kelvin-Voigt model
• nonlinear Galerkin method
• spectral approximations
• a priori error bound
• uniform convergence in time

In this paper, a variant of nonlinear Galerkin method is proposed and analysed for equations of motions arising in a Kelvin-Voigt model of viscoelastic fluids in a bounded spatial domain in IRd (d = 2, 3). Some new a priori bounds are obtained for the exact solution when the forcing function is independent of time or belongs to L-infinity in time. As a consequence, existence of a global attractor is shown. For the spectral Galerkin scheme, existence of a unique discrete solution to the semidiscrete scheme is proved and again existence of a discrete global attractor is established. Further, optimal error estimate in L-infinity(L-2) and L-infinity(H-0(1))-norms are proved. Finally, a modified nonlinear Galerkin method is developed and optimal error bounds are derived. It is, further, shown that error estimates for both schemes are valid uniformly in time under uniqueness condition.

• 出版日期2014