On the coupling of local discontinuous Galerkin and boundary element methods for non-linear exterior transmission problems
On the coupling of local discontinuous Galerkin and boundary element methods for non-linear exterior transmission problems
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DOI：
10.1093/imanum/drm019
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发表时间：
2007-09
影响因子：
2.1
通讯作者：
R. Bustinza;G. Gatica;F. Sayas
中科院分区：
文献类型：
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作者：
R. Bustinza;G. Gatica;F. Sayas
本文应用局部间断Galerkin法和边界元法耦合求解一类平面非线性外传播问题。作为一个模型，我们考虑一个非线性椭圆方程在一个环形多边形区域耦合的泊松方程在周围的无界外部区域。此外，我们假设界面边界上的不连续传输条件。我们的方法构成了一个扩展到非线性问题的先验误差分析最近开发的线性外部传输问题。这里采用的大多数技术与线性情况相似，但也存在一些差异。特别是，由于非均匀传输条件，所谓的数值通量需要适当定义。我们证明了稳定的离散计划相对于一个网格依赖的规范，并得出一个奇怪的相关误差的类型估计。然后，我们利用离散空间的局部和整体逼近性质，得到了能量范数下的先验误差估计。
In this paper, we apply the coupling of local discontinuous Galerkin and boundary element methods to solve a class of non-linear exterior transmission problems in the plane. As a model, we consider a non-linear elliptic equation in an annular polygonal domain coupled with the Poisson equation in the surrounding unbounded exterior region. In addition, we assume discontinuous transmission conditions on the interface boundary. Our approach constitutes an extension to non-linear problems of the a priori error analysis developed recently for linear exterior transmission problems. Most of the techniques employed here are similar to the linear case but some differences appear. In particular, because of the non-homogeneous transmission conditions, the so-called numerical fluxes need to be suitably defined. We prove stability of the resulting discrete scheme with respect to a mesh-dependent norm and derive a Strang-type estimate for the associated error. Then, we apply local and global approximation properties of the discrete spaces to obtain the a priori error estimates in the energy norm.