LINEARIZATION OF A NONLINEAR PERIODIC BOUNDARY CONDITION RELATED TO CORROSION MODELING

• 来源期刊: 计算数学（英文版）
• 关键词: Galvanic corrosion Homogenization Nonlinear elliptic boundary value problem Butler-Volmer boundary condition Robin boundary condition
• 年，卷（期）: 2007,（6）
• 页码范围: 645-660
• 页数: 16页
• 语种: 英文

摘要

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two and three-dimensional case and provide two-dimensional numerical experiments.