论文标题
适用于抛物线问题的自适应非等级盖尔金方法应用于移动网格和虚拟元素方法
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
论文作者
论文摘要
我们提出了线性抛物线问题不一致和非层次盖尔金方法的后验误差估计，从而使它们首次与非常通用的网格修饰一起使用。我们将非等级的方案视为在连续时间阶段使用的空间galerkin空间可能完全无关。通过将我们的结果应用于移动网格的有限元方法并使用估算器在任意多边形网格上基于虚拟元素方法来驱动自适应算法，从而证明了这种设置的实际兴趣。对于$ l^2（h^1）$和$ l^{\ infty}（l^2）$规范的错误估计的A后验错误估计是使用椭圆形重建技术得出的，该技术是在抽象的框架中旨在精确地封装了我们对不一致的概念和非层次结构的概念，并进行了层次的概念，并进行了层次的概念，并进行了层次的概念，并进行了层次的概念，并进行了层次的概念，并进行了计算的效率，显着放松了先前估计的基本假设。
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes which are non-hierarchical in the sense that the spatial Galerkin spaces used on consecutive time-steps may be completely unrelated from one another. The practical interest of this setting is demonstrated by applying our results to finite element methods on moving meshes and using the estimators to drive an adaptive algorithm based on a virtual element method on a mesh of arbitrary polygons. The a posteriori error estimates, for the error measured in the $L^2(H^1)$ and $L^{\infty}(L^2)$ norms, are derived using the elliptic reconstruction technique in an abstract framework designed to precisely encapsulate our notion of inconsistency and non-hierarchicality and requiring no particular compatibility between the computational meshes used on consecutive time-steps, thereby significantly relaxing this basic assumption underlying previous estimates.
