A composite h-p discontinuous Galerkin finite element discretization of a diffusion problem, where subdomains are separated by thin membranes, modeled by the Kedem–Katchalsky transmission condition, is considered. A preconditioner based on the additive Schwarz method is proved to have the condition number bounded independently of the mesh size, the membrane permeability and the diffusion coefficient, provided the subspace solvers have their condition numbers bounded as well. Numerical experiments confirm these findings and additionally indicate the convergence rate is only weakly dependent on the degree of the approximating polynomials.

中文翻译：

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基于 Kedem-Katchalsky 传输条件的膜扩散问题的预处理器分析

考虑了扩散问题的复合h - p不连续 Galerkin 有限元离散化，其中子域由薄膜分隔，由 Kedem-Katchalsky 传输条件建模。如果子空间求解器的条件数也有界，则基于加性 Schwarz 方法的预处理器被证明具有独立于网格尺寸、膜渗透率和扩散系数的条件数。数值实验证实了这些发现，并另外表明收敛速度仅微弱地依赖于近似多项式的程度。