Convection‐adapted BEM‐based FEM
Convection‐adapted BEM‐based FEM
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基于对流的 BEM 有限元法
DOI：
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发表时间：
2015
期刊：
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通讯作者：
Steffen Weißer
中科院分区：
文献类型：
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作者：
C. Hofreither;U. Langer;Steffen Weißer
本文提出了一种新的三维对流扩散反应边值问题的离散方法，该方法采用PDE调和形函数在多面体单元上进行离散。采用局部边界元法构造单元刚度矩阵。我们的方法，我们称之为基于边界元的有限元法，因此可以被认为是一个局部Trefftz方法与单元方式（局部）PDE调和形函数。这些形状函数的Dirichlet边界数据是根据对流适应程序选择的，该程序求解PDE在单元边和面上的投影。与标准FEM和以前的基于边界元的FEM方法相比，这提高了对流占优问题离散化方法的稳定性，正如我们在几个数值实验中所证明的那样。我们的实验还表明，我们提出的方法相比，SUPG方法的指数层在流出边界的分辨率提高。
We present a new discretization method for convection‐diffusion‐reaction boundary value problems in 3D with PDE‐harmonic shape functions on polyhedral elements. The element stiffness matrices are constructed by means of local boundary element techniques. Our method, which we refer to as a BEM‐based FEM, can therefore be considered as a local Trefftz method with element‐wise (locally) PDE‐harmonic shape functions. The Dirichlet boundary data for these shape functions is chosen according to a convection‐adapted procedure which solves projections of the PDE onto the edges and faces of the elements. This improves the stability of the discretization method for convection‐dominated problems both when compared to a standard FEM and to previous BEM‐based FEM approaches, as we demonstrate in several numerical experiments. Our experiments also show an improved resolution of the exponential layer at the outflow boundary for our proposed method when compared to the SUPG method.