Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders. (English. Russian original) Zbl 1442.76013
Comput. Math. Math. Phys. 58, No. 7, 1099-1115 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 7 (2018).
Summary: An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution – the error of approximation method and the round-off error – are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.
MSC:
| 76A10 | Viscoelastic fluids |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
polymer fluid dynamics; algorithm without saturation; Chebyshev polynomials; collocation method; error estimates; exponential convergenceReferences:
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