| AN ITERATIVE HYBRIDIZED MIXED FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS |
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| 作者姓名： | Dai-quYang JenniferZhao |
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| 作者单位： | [1]DepartmentofMathematics,WayneStateUniversity,Detroit,MI48202,USA [2]DepartmentofMathematicsandStatistics,UniversityofMichigan-Dearborn,Dearborn,MI48128,USA |
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| 摘 要： | An iterative algorithm is proposed and analyzed based on a hybridized mized finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions,conormal derivatives,and coefficients.This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence ,following the idea of Schwarz Alternating Methods,Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen,Numeric exper-iments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients.In contrast to standard numerical methods,the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases.
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| 关 键 词： | 迭代杂交有限元法 椭圆界面问题 强不连续系数 不连续解 Schwarz交替法 误差估计 精度 Stefan问题 合金凝固问题 熔解温度 偏微分方程 多相不融合流 匹配格 数值算例 |
AN ITERATIVE HYBRIDIZED MIXED FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS |
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| Dai-quYang JenniferZhao.AN ITERATIVE HYBRIDIZED MIXED FINITE ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS[J].Journal of Computational Mathematics,2003,21(3):257-276. |
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| Authors: | Dao-Qi Yang |
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| Abstract: | An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions, conormal derivatives, and coefficients. This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence, following the idea of Schwarz Alternating Methods. Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients. In contrast to standard numerical methods, the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases. |
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| Keywords: | Mixed finite element method Interface problems Discontinuous solutions |
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