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We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal…

Numerical Analysis · Mathematics 2017-11-17 Muhammad Ilyas , Bishnu P. Lamichhane

In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…

Numerical Analysis · Mathematics 2024-06-13 David Mora , Jesus Vellojin , Nitesh Verma

Trimming is a common operation in CAD, 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…

Numerical Analysis · Mathematics 2021-02-11 Annalisa Buffa , Riccardo Puppi , Rafael Vázquez

In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…

Numerical Analysis · Mathematics 2024-01-30 Thirupathi Gudi , Ramesh Chandra Sau

We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties…

Numerical Analysis · Mathematics 2025-08-18 Cu Cui , Guido Kanschat

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…

Numerical Analysis · Mathematics 2022-06-22 Mathias Anselmann , Markus Bause

We present and analyze a cut finite element method for the weak imposition of the Neumann boundary conditions of the Darcy problem. The Raviart-Thomas mixed element on both triangular and quadrilateral meshes is considered. Our method is…

Numerical Analysis · Mathematics 2021-11-22 Riccardo Puppi

Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival owing to its natural application in modern computational…

Numerical Analysis · Mathematics 2025-05-13 Hiroki Ishizaka

In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique…

Numerical Analysis · Mathematics 2016-10-17 Thomas Boiveau , Erik Burman , Susanne Claus , Mats G. Larson

In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved…

Numerical Analysis · Mathematics 2023-04-05 Silvia Bertoluzza , Micol Pennacchio , Daniele Prada

For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…

Numerical Analysis · Mathematics 2021-04-07 Jan Helmig , Fabian Key , Marek Behr , Stefanie Elgeti

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…

Numerical Analysis · Mathematics 2016-01-20 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

In many situations with finite element discretizations it is desirable or necessary to impose boundary or interface conditions not as essential conditions -- i.e. through the finite element space -- but through the variational formulation.…

Numerical Analysis · Mathematics 2016-03-03 Christoph Lehrenfeld

Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element…

Computational Engineering, Finance, and Science · Computer Science 2020-01-30 Nathan Sime , Cian R. Wilson

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

Numerical Analysis · Mathematics 2021-01-19 Xiaoxiao He , Fei Song , Weibing Deng

In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two…

Numerical Analysis · Mathematics 2015-09-03 Thomas Boiveau

In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the…

Numerical Analysis · Mathematics 2014-01-06 Sébastien Court , Michel Fournié , Alexei Lozinski

We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element…

Numerical Analysis · Mathematics 2026-05-01 Tom Gustafsson , Antti Hannukainen , Vili Kohonen , Juha Videman

The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…

Numerical Analysis · Mathematics 2025-12-16 Michael Neilan , Maxim Olshanskii , Henry von Wahl

The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…

Numerical Analysis · Mathematics 2017-04-24 Johnny Guzmán , Maxim Olshanskii