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Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…
We propose a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh. The dependent variables of velocity, pressure…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
Nitsche's method is a well-established approach for weak enforcement of boundary conditions for partial differential equations (PDEs). It has many desirable properties, including the preservation of variational consistency and the fact that…
The weak imposition of essential boundary conditions is an integral aspect of unfitted finite element methods, where the physical boundary does not in general coincide with the computational domain. In this regard, the symmetric Nitsche's…
Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of…
We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as…
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…
A Nitche's method is presented to couple non-conforming two and three dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for elastic stress analyses under the static…
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty…
Nitsche's method is a standard device for weakly imposing Dirichlet boundary conditions, but for the stabilized nonsymmetric formulation the available $L^2$-error analysis for Poisson's equation still predicts a half-order loss, whereas…
We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems,…
We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell…
In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities of general geometry. The proposed method does not require the background mesh to fit the interfaces of impurities, and…
The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…
We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms…
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.…
A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates,…