Related papers: On Nitsche's method for elastic contact problems
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
This work establishes a solution to the problem of assessing the capacity of multi-object assemblies to withstand external forces without becoming unstable. Our physically-grounded approach handles arbitrary structures made from rigid…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…
We develop a Nitsche finite element method for a model of Euler--Bernoulli beams with axial stiffness embedded in a two--dimensional elastic bulk domain. The beams have their own displacement fields, and the elastic subdomains created by…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
This paper addresses the local recovery of conservative fluxes and the a posteriori error analysis for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed by means of…
In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
In this paper an abstract evolutionary hemivariational inequality with a history-dependent operator is studied. First, a result on its unique solvability and solution regularity is proved by applying the Rothe method. Next, we introduce a…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
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.…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the Frank-Oseen elastic free-energy model of nematic and cholesteric liquid crystals, where the required unit-length…
We study the Stokes--Poisson--Boltzmann equations with Dirichlet and Navier boundary conditions. The system consists of the incompressible Stokes equations coupled with a nonlinear Poisson--Boltzmann equation through electrostatic forcing…
We propose to combine the ideas of mass redistribution and component mode synthesis. More specifically, we employ the MacNeal method, which readily leads to a singular mass matrix, and an accordingly modified version of the Craig-Bampton…
In this paper, a residual-type a posteriori error estimator is proposed and analyzed for a modified weak Galerkin finite element method solving linear elasticity problems. The estimator is proven to be both reliable and efficient because it…
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,…
We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in…