13 research outputs found
A note on the penalty parameter in Nitsche's method for unfitted boundary value problems
Nitsche's method is a popular approach to implement Dirichlet-type boundary
conditions in situations where a strong imposition is either inconvenient or
simply not feasible. The method is widely applied in the context of unfitted
finite element methods. From the classical (symmetric) Nitsche's method it is
well-known that the stabilization parameter in the method has to be chosen
sufficiently large to obtain unique solvability of discrete systems. In this
short note we discuss an often used strategy to set the stabilization parameter
and describe a possible problem that can arise from this. We show that in
specific situations error bounds can deteriorate and give examples of
computations where Nitsche's method yields large and even diverging
discretization errors
A Nitsche-based cut finite element method for a fluid--structure interaction problem
We present a new composite mesh finite element method for fluid--structure
interaction problems. The method is based on surrounding the structure by a
boundary-fitted fluid mesh which is embedded into a fixed background fluid
mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The
coupling between the embedded and background fluid meshes is enforced using a
stabilized Nitsche formulation which allows us to establish stability and
optimal order \emph{a priori} error estimates,
see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state
fluid--structure interaction problem where a hyperelastic structure interacts
with a viscous fluid modeled by the Stokes equations. We evaluate an iterative
solution procedure based on splitting and present three-dimensional numerical
examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in
CAMCo
A note on the stability parameter in Nitsche's method for unfitted boundary value problems
Nitsche's method is a popular approach to implement Dirichlet-type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible. The method is widely applied in the context of unfitted finite element methods. Of the classical (symmetric) Nitsche's method it is well-known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems. In this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this. We show that in specific situations error bounds can deteriorate and give examples of computations where Nitsche's method yields large and even diverging discretization errors. <br/