相关论文: A New Least Squares Stabilized Nitsche Method for …
We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces in multi-ply multi-directional composite laminates. In…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
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…
The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…
In this paper we use the Isogeometric method to solve the Helmholtz equation with nonhomogeneous Dirichlet boundary condition over a bounded physical domain. Starting from the variational formulation of the problem, we show with details how…
This paper studies a new gradient regularity in Lorentz spaces for solutions to a class of quasilinear divergence form elliptic equations with nonhomogeneous Dirichlet boundary conditions: \begin{align*} \begin{cases} div(A(x,\nabla u)) &=…
We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
In this paper we consider the finite element approximation of Maxwell's problem and analyse the prescription of essential boundary conditions in a weak sense using Nitsche's method. To avoid indefiniteness of the problem, the original…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming $C^1$-continuous finite elements. We implement the…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…
We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…
We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…
In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the $H^1$- and…
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…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…
We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are $C^1$ elements obtained by taking tensor products of Hermite splines. The formulation is based on Nitsche's method for weak enforcement of…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
We design a cut finite element method for the incompressible Stokes equations on curved domains. The cut finite element method allows for the domain boundary to cut through the elements of the computational mesh in a very general fashion.…
We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilised finite element method…