A Partition of Unity construction of the stabilization function in Nitsche’s method for variational problems

In this paper we develop a partition-of-unity construction of the stabilization function required in Nitsche’s method, which can be seen as a generalization of the element-wise construction that is widely used in finite element methods. This allows for the use of Nitsche’s method within the Partitio...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2024-06, Vol.426, p.117002, Article 117002
Main Authors: Jiménez Recio, Pablo, Schweitzer, Marc Alexander
Format: Article
Language:English
Subjects:
Essential boundary conditions
Meshfree method
Nitsche’s method
Partition of unity method
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Summary:In this paper we develop a partition-of-unity construction of the stabilization function required in Nitsche’s method, which can be seen as a generalization of the element-wise construction that is widely used in finite element methods. This allows for the use of Nitsche’s method within the Partition of Unity Method with a stabilization function that is not simply a constant over the whole boundary. In addition to that, we introduce a patch-aggregation approach designed to avoid arbitrarily large values of the stabilization function and the associated ill-conditioned systems and deteriorated convergence rates. We present numerical results to validate the proposed methods, covering Dirichlet boundary conditions, interface constraints and higher-order problems. These results clearly show that our approach leads to optimal convergence rates.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2024.117002