2017/11/22 by Herbert Egger, Egger, Herbert, Christoph Erath +3
Computer Science · Engineering · Mathematics · #65N12 #65N15 #65N30 #65N38 #65N40 #82B24 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1711.08487
openalex publication_date 2017/11/22 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider the numerical approximation of parabolic-elliptic interface\nproblems by the non-symmetric coupling method of MacCamy and Suri [Quart. Appl.\nMath., 44 (1987), pp. 675--690]. We establish well-posedness of this\nformulation for problems with non-smooth interfaces and prove quasi-optimality\nfor a class of conforming Galerkin approximations in space. Therefore, error\nestimates with optimal order can be deduced for the semi-discretization in\nspace by appropriate finite and boundary elements. Moreover, we investigate the\nsubsequent discretization in time by a variant of the implicit Euler method. As\nfor the semi-discretization, we establish well-posedness and quasi-optimality\nfor the fully discrete scheme under minimal regularity assumptions on the\nsolution. Error estimates with optimal order follow again directly. Our\nanalysis is based on estimates in appropriate energy norms. Thus, we do not use\nduality arguments and corresponding estimates for an elliptic projection which\nare not available for the non-symmetric coupling method. Additionally, we\nprovide again error estimates under minimal regularity assumptions. Some\nnumerical examples illustrate our theoretical results.\n