A Newton-Finite Difference Method for Elliptic and Parabolic Problems With Nonlinear Interface Jump Conditions
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| Publicado en: | ProQuest Dissertations and Theses (2025) |
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| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| 100 | 1 | |a Gakii, Sarah | |
| 245 | 1 | |a A Newton-Finite Difference Method for Elliptic and Parabolic Problems With Nonlinear Interface Jump Conditions | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a Many real-world scientific and engineering applications often involve interface problems characterized by discontinuous coefficients and nonlinear interface conditions. Mathematically, these conditions lead to differential equations in which the solution or its derivatives may be discontinuous or lack smoothness across interfaces, typically corresponding to material boundaries. These discontinuities present significant challenges for numerical solutions. As such, developing robust and effective computational methods is critical for capturing the complex behaviors present in these systems and for producing accurate, reliable simulations.This research focuses on the formulation and implementation of a Newton-finite difference method designed to address nonlinear elliptic and parabolic interface problems, where the nonlinearity occurs at the interface. To simplify implementation while preserving accuracy and reliability, the method employs a fitted mesh approach, aligning the grid with the interface.To evaluate its performance, the method is tested against a series of theoretical benchmarks and practical models. The results highlight the method's accuracy, stability, and computational efficiency; demonstrating its potential as a reliable alternative for solving interface problems in scientific and engineering contexts. | |
| 653 | |a Mathematics | ||
| 653 | |a Theoretical mathematics | ||
| 653 | |a Applied mathematics | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3245580512/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3245580512/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |