Related papers: $L^2$-error estimates for finite element approxima…

This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…

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,…

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 show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…

This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson…

We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition…

In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$.…

$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…

In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…

We derive a priori error estimates for semidiscrete finite element approximations of stable solutions to time-dependent mean field game systems with Dirichlet boundary conditions. Expressing solutions to the MFG system as zeros of a…

In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully discrete problem, where a discontinuous Galerkin method in time…

The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We…

We prove quasi-optimal $L^\infty$ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming…

In \cite{cheung2019optimally}, the authors presented two finite element methods for approximating second order boundary value problems on polytopial meshes with optimal accuracy without having to utilize curvilinear mappings. This was done…

In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the…

This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…

This paper proves error estimates for $H^2$ conforming finite elements for equations which model the flow of surfaces by different powers of the mean curvature (this includes mean curvature flow). for an adapted scheme originally proposed…

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…