论文标题
兼容嵌入式杂交的不连续的galerkin方法用于Stokes-darcy-transport问题
A compatible embedded-hybridized discontinuous Galerkin method for the Stokes--Darcy-transport problem
论文作者
论文摘要
我们提出了嵌入式杂交不连续的Galerkin（EDG-HDG）的有限元方法的稳定性和误差分析，用于耦合的Stokes--darcy流和运输。由Stokes-darcy方程控制的流问题被最近引入的质量保护EDG-HDG方法离散，而嵌入式不连续的Galerkin（EDG）方法用于离散传输方程。我们表明，耦合流和运输离散化是兼容且稳定的。此外，我们显示了半污垢传输问题的存在和独特性，并产生了最佳的先验错误估计。我们提供了说明理论结果的数值示例。特别是，我们将兼容的EDG-HDG离散化与耦合stokes的离散化（不兼容的运输问题）进行了比较。我们证明，在不兼容的离散化可能导致转运问题解决方案中的虚假振荡的地方，兼容的离散化无振荡。还提供了一个具有现实参数的其他数值示例。
We present a stability and error analysis of an embedded-hybridized discontinuous Galerkin (EDG-HDG) finite element method for coupled Stokes--Darcy flow and transport. The flow problem, governed by the Stokes--Darcy equations, is discretized by a recently introduced exactly mass conserving EDG-HDG method while an embedded discontinuous Galerkin (EDG) method is used to discretize the transport equation. We show that the coupled flow and transport discretization is compatible and stable. Furthermore, we show existence and uniqueness of the semi-discrete transport problem and develop optimal a priori error estimates. We provide numerical examples illustrating the theoretical results. In particular, we compare the compatible EDG-HDG discretization to a discretization of the coupled Stokes--Darcy and transport problem that is not compatible. We demonstrate that where the incompatible discretization may result in spurious oscillations in the solution to the transport problem, the compatible discretization is free of oscillations. An additional numerical example with realistic parameters is also presented.
