Adaptive discontinuous Galerkin methods for elliptic interface problems
Adaptive discontinuous Galerkin methods for elliptic interface problems
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DOI：
10.1090/mcom/3322
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
A. Cangiani;E. Georgoulis;Younis A. Sabawi
中科院分区：
文献类型：
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作者：
A. Cangiani;E. Georgoulis;Younis A. Sabawi
考虑了一种内罚不连续伽辽金 (dG) 方法，用于解决椭圆界面问题，可能涉及弯曲界面，具有通量平衡界面条件，例如模拟溶质通过半透膜的传质。该方法允许使用极其通用的弯曲元件形状来精确解析界面几何形状。提出了该 dG 方法的残差型后验误差估计器，并证明了相应 dG 能量范数中误差的上限和下限。随后使用后验误差界来证明基本的先验收敛结果。所提出的理论得到了一系列数值实验的补充。所提出的方法也立即适用于具有非必要边界条件的弯曲域的情况。
An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with flux-balancing interface conditions, e.g., modelling mass transfer of solutes through semipermeable membranes, is considered. The method allows for extremely general curved element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.