CutFEM: Foundations, Stabilization, and Applications
【2026.10.20 10:00-11:00，蓝白楼311】 |
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2026.10.13 Colloquia Seminars
| Speaker |
Prof. Mats G Larson, Umeå universitet |
| Title |
CutFEM: Foundations, Stabilization, and Applications |
| Time |
2026.10.20 10:00-11:00 |
| Venue |
蓝白楼311 |
| Abstract |
Cut finite element methods (CutFEM) provide a flexible framework for discretizing partial differential equations on meshes that need not conform to domain boundaries or interfaces. This talk gives an overview of the basic ideas for problems posed in bulk domains, on embedded surfaces, and on mixed-dimensional domains, coupling components of different dimensions.
We introduce the main ingredients of CutFEM discretizations, including the treatment of boundary and interface conditions, and outline a general analytical framework for establishing stability, error estimates, and bounds on the condition number. A central theme is robustness with respect to how the geometry intersects the background mesh. We discuss both weak stabilization through ghost penalties and strong stabilization through discrete extension, highlighting their principles and connections.
Several examples illustrate the methodology across different geometric settings, including applications to industrial CAD models. These examples demonstrate how CutFEM combines flexibility in geometric representation with accurate and robust numerical approximation. |
| Biography |
Professor Mats G. Larson is Professor of Applied Mathematics at Umeå University, Sweden. He is internationally recognized for his contributions to finite element analysis, particularly in unfitted finite element methods (CutFEM), stabilized finite element methods, and numerical methods for partial differential equations on complex geometries. Jointly with E. Burman, P. Hansbo, and S. Zahedi, he published the authoritative survey article “Cut Finite Element Methods” in Acta Numerica (2025), which provides a comprehensive overview of the theory, development, and applications of CutFEM. He is also the author, together with F. Bengzon, of the influential textbook The Finite Element Method: Theory, Implementation, and Applications, widely used in graduate education and research in computational mathematics. | |
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