An adaptive least-squares finite element method for Giesekus viscoelastic flow problems
An adaptive least-squares finite element method for Giesekus viscoelastic flow problems
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DOI：
10.1080/00207160.2020.1865532
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发表时间：
2021-01-14
影响因子：
1.8
通讯作者：
Lee, Hyesuk
中科院分区：
文献类型：
--
作者：
Lee, Hsueh-Chen;Lee, Hyesuk
在这项研究中，最小二乘（LS）有限元方法与自适应网格的方法进行了研究Giesekus粘弹性流动问题。考虑牛顿线性化粘弹性问题在均匀网格和自适应网格上的加权LS方法，其中自适应网格由最小二乘解自动生成。我们使用一个剩余型后验误差估计来调整LS泛函中的权重，并比较使用不同分级函数生成的自适应网格的收敛行为。数值结果表明，当所有变量采用等阶线性插值函数时，自适应LS方法至少具有一阶收敛速度，这与理论估计一致.此外，自适应网格生成的速度优于那些基于后验误差估计，产生更好的数值结果。
In this study, a least-squares (LS) finite element method with an adaptive mesh approach is investigated for Giesekus viscoelastic flow problems. We consider the weighted LS method on uniform and adaptive meshes for the Newton linearized viscoelastic problem, where adaptive grids are automatically generated by the least-squares solutions. We use a residual-type a-posteriori error estimator to adjust weights in the LS functional and compare the convergence behaviour of adaptive meshes generated using different grading functions. Numerical results demonstrate that the adaptive LS method shows at least the first-order convergence rate when equal-order linear interpolation functions are used for all variables, which agrees with the theoretical estimate. In addition, adaptive grids generated using the velocity outperform those based on the a-posteriori error estimator, yielding better numerical results.