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On the solvability of the nonlinear problems in an algebraically stabilized finite element method for evolutionary transport-dominated equations
Mathematics of Computation ( IF 2.2 ) Pub Date : 2020-11-16 , DOI: 10.1090/mcom/3576 Volker John , Petr Knobloch , Paul Korsmeier
Mathematics of Computation ( IF 2.2 ) Pub Date : 2020-11-16 , DOI: 10.1090/mcom/3576 Volker John , Petr Knobloch , Paul Korsmeier
Abstract:The so-called FEM-FCT (finite element method flux-corrected transport) scheme for evolutionary scalar convection-dominated equations
leads in each time instant to a nonlinear problem. For sufficiently small time steps, the existence and uniqueness of a solution of these problems is shown. Moreover, the convergence of a semi-smooth Newton's method is studied.
中文翻译：
演化控制方程的代数稳定有限元方法中非线性问题的可解性
摘要：求解标量对流占优方程的所谓FEM-FCT（有限元通量校正输运）方案
在每个时刻都会导致非线性问题。对于足够小的时间步长，显示了这些问题的解决方案的存在和唯一性。此外，研究了半光滑牛顿法的收敛性。
更新日期：2021-01-05
leads in each time instant to a nonlinear problem. For sufficiently small time steps, the existence and uniqueness of a solution of these problems is shown. Moreover, the convergence of a semi-smooth Newton's method is studied.
中文翻译：
演化控制方程的代数稳定有限元方法中非线性问题的可解性
摘要：求解标量对流占优方程的所谓FEM-FCT（有限元通量校正输运）方案
在每个时刻都会导致非线性问题。对于足够小的时间步长，显示了这些问题的解决方案的存在和唯一性。此外，研究了半光滑牛顿法的收敛性。
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