A New Least Squares Stabilized Nitsche Method for Cut Isogeometric Analysis

Abstract

We derive a new stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis (CutIGA). We consider $C^1$ splines and stabilize the standard Nitsche method by adding certain elementwise least squares terms in the vicinity of the Dirichlet boundary and an additional term on the boundary which involves the tangential gradient. We show coercivity with respect to the energy norm for functions in $H^2(\Omega )$ and optimal order a priori error estimates in the energy and $L^2$ norms. To obtain a well posed linear system of equations we combine our formulation with basis function removal which essentially eliminates basis functions with sufficiently small intersection with $\Omega$. The upshot of the formulation is that only elementwise stabilization is added in contrast to standard procedures based on ghost penalty and related techniques and that the stabilization is consistent. In our numerical experiments we see that the method works remarkably well in even extreme cut situations using a Nitsche parameter of moderate size.

References in corpus (6)

• Condition number analysis and preconditioning of the finite cell method
• The aggregated unfitted finite element method for elliptic problems
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• A note on the penalty parameter in Nitsche's method for unfitted boundary value problems
• CutIGA with Basis Function Removal
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Cited by in corpus (9)

• Isogeometric Analysis on V-reps: first results
• A minimal stabilization procedure for Isogeometric methods on trimmed geometries
• Reissner-Mindlin shell theory based on tangential differential calculus
• The Finite Cell Method with Least Squares Stabilized Nitsche Boundary Conditions
• Cut Topology Optimization for Linear Elasticity with Coupling to Parametric Nondesign Domain Regions
• A localized reduced basis approach for unfitted domain methods on parameterized geometries
• Fast parametric analysis of trimmed multi-patch isogeometric Kirchhoff-Love shells using a local reduced basis method
• Graded Parametric CutFEM and CutIGA for Elliptic Boundary Value Problems in Domains with Corners
• Robust Trimmed Multipatch IGA with Singular Maps