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A modified nonlinear Galerkin method for the viscoelastic fluid motion equations. (English) Zbl 1210.76111

Summary: We first provide a priori estimates of the solution for the nonstationary two-dimensional viscoelastic fluid motion equations with periodic boundary condition. We then present an modified nonlinear Galerkin method for solving such equations. By comparing the convergence rates of the proposed method with the standard Galerkin method, we conclude that the modified nonlinear Galerkin method is better than the standard Galerkin method because the former can save a large amount of computational work and maintain the convergence rate of the latter.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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References:

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