A large time stepping viscosity-splitting finite element method for the viscoelastic flow problem

作者：Zhang Tong^*; Pedro Damazio; Yuan JinYun

来源：Advances in Computational Mathematics, 2015, 41(1): 149-190.

DOI：10.1007/s10444-014-9353-4

• Viscoelastic flow problem
• Viscosity-splitting method
• Large time stepping
• Stability
• Convergence
• Optimal error estimates

In this article, a large time stepping viscosity-splitting scheme is considered for the viscoelastic flow problem. The temporal term is decomposed into a sequence of two steps (using decomposition of the viscosity). For the first step, a linear elliptic problem is solved with explicit scheme for the convection term (a linear system with a constant coefficient matrix is obtained and the computation becomes easy). At the second step, the problem has the structure of the Stokes problem. Both two problems satisfy the homogeneous Derichlet boundary conditions for the velocities. The main novelties of this work are the stability of numerical solutions under the condition k (1) Delta t a parts per thousand currency sign 1 with a positive constant k (1), and optimal error estimates for both velocity in L (a)(H (1)) and L (2)(H (1)) norms and pressure in L (a)(L (2)) and L (2)(L (2)) norms. In order to enlarge the time step, we introduce a diffusion term theta Delta u in all steps of the schemes. Finally, some numerical results are provided to display the performance of our algorithm.

• 出版日期2015-2
• 单位河南理工大学