AN ITERATIVE HYBRIDIZED MIXED FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Mixed finite element method Interface problems Discontinuous solutions.
• 年，卷（期）: 2003,（3）
• 页码范围: 257-276
• 页数: 20页
• 分类号: O1
• 语种: 英文

摘要

An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems withstrongly discontinuous solutions, conormal derivatives, and coefficients. This algorithmiteratively solves small problems for each single phase with good accuracy and exchangeinformation at the interface to advance the iteration until convergence, following the ideaof Schwarz Alternating Methods. Error estimates are derived to show that this algorithmalways converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases areperformed to show the accuracy of the method for capturing discontinuities in the solutionsand coefficients. In contrast to standard numerical methods, the accuracy of our methoddoes not seem to deteriorate as the coefficient discontinuity increases.