论文标题
分析进化方程式和应用的完全差异，不合格的近似
Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications
论文作者
论文摘要
在本文中，我们考虑了部署不合格的空间近似和有限时间差异的抽象演化方程的完全差异近似（Rothe-Galerkin方法）。主要结果是离散解决方案与连续问题的弱解决方案的收敛性。因此，可以将结果解释为数值方法的理由，也可以将其解释为构建弱解决方案的替代方法。我们在所谓的不合格的Bochner伪超声酮操作员的非常通用和抽象的设置中提出了问题，该操作员允许对几种进化问题进行统一的处理。我们对不合格的Bochner伪超声酮操作员的抽象结果允许仅通过验证对操作员的一些自然假设和离散空间来建立（弱）收敛。因此，可以轻松执行其他几个进化问题的应用和扩展。我们体现了我们的方法在多个DG方案上的适用性，以解决不稳定的$ p $ -navier-stokes问题。最后一部分报告了一些数值实验的结果。
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Therefore, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We formulate the problem in the very general and abstract setting of so-called non-conforming Bochner pseudo-monotone operators, which allows for a unified treatment of several evolution problems. Our abstract results for non-conforming Bochner pseudo-monotone operators allow to establish (weak) convergence just by verifying a few natural assumptions on the operators time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be performed easily. We exemplify the applicability of our approach on several DG schemes for the unsteady $p$-Navier-Stokes problem. The results of some numerical experiments are reported in the final section.
