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A MINIMAL STABILIZATION PROCEDURE FOR ISOGEOMETRIC METHODS ON TRIMMED GEOMETRIES.
- Source :
- SIAM Journal on Numerical Analysis; 2020, Vol. 58 Issue 5, p2711-2735, 25p
- Publication Year :
- 2020
-
Abstract
- Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming, the geometric description of the patch remains unchanged, but the underlying mesh is unfitted with the physical object. We discuss the main problems arising when solving elliptic PDEs on a trimmed domain. First we prove that, even when Dirichlet boundary conditions are weakly enforced using Nitsche's method, the resulting method suffers lack of stability. Then, we develop novel stabilization techniques based on a modification of the variational formulation, which allow us to recover well-posedness and guarantee accuracy. Optimal a priori error estimates are proven, and numerical examples confirming the theoretical results are provided. [ABSTRACT FROM AUTHOR]
- Subjects :
- COMPUTER-aided design
ISOGEOMETRIC analysis
GEOMETRY
FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 58
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 147633638
- Full Text :
- https://doi.org/10.1137/19M1244718