在圆问题中的多边形网格上的不连续的Galerkin方法中的后续误差近似
1Chair for Computational Engineering, Faculty of Civil Engineering, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland. jan.jaskowiec@pk.edu.pl.
本研究引入了一种新的后续误差近似,用于二维不连续的加勒金 (DG) 方法. 该方法有效地估计了使用多边形元素的数值模拟中的错误,有助于改进自适应网格.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 科学计算科学计算
背景情况:
- 后期错误估计对于评估数值方法的准确性至关重要.
- 不连续的加勒金 (DG) 方法在处理复杂的几何形状和解决方案特性方面提供了灵活性.
- 现有的 DG 方法通常依赖于内部惩罚方法,激励探索替代配方.
研究的目的:
- 为二维不连续的Galerkin (DG) 方法开发和介绍一个新的后续误差近似概念.
- 为了有效的错误估计,利用剩余和独特的 DG 属性.
- 为了证明开发的方法在多边形网格和适应式hp精炼上的适用性.
主要方法:
- 这项研究采用了不连续的加勒金方法,以有限差异 (DGFD) 强制解决方案的连续性.
- 错误近似是使用层次基础函数在丰富空间中构建的.
- 多边形有限元素,包括四边形和三角形元素,都被考虑在DG框架内.
主要成果:
- 分析了涉及Poisson和线性弹性问题的基准示例.
- 错误估计地图显示,在各种网格密度和近似顺序中,与精确错误有很强的相关性.
- 提出的错误近似概念已成功应用于自适应式hp网状精细化.
结论:
- 提出的后续误差近似概念是简单的,有效的,并利用DG方法属性.
- 采用多边形元素的 DGFD 方法为错误估计提供了一个强大的框架.
- 该方法在复杂的模拟中显示了适应性网状精炼策略的前景.
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