Related papers: Discrete reliability for high-order Crouzeix--Ravi…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…
We present a numerical investigation of residual-based a posteriori error estimation for finite element discretizations of convection--diffusion equations stabilized by algebraic flux correction and related algebraic stabilization…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
In this paper we will develop a family of non-conforming "Crouzeix-Raviart" type finite elements in three dimensions. They consist of local polynomials of maximal degree $p\in\mathbb{N}$ on simplicial finite element meshes while certain…
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regularity analysis of weak solutions under minimal assumptions on…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary…
This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…
We show that the DDR method can be interpreted as defining a computable consistent discrete $\mathrm{L}^2$ product on a conforming FES defined by PDEs. Without modifying the numerical method itself, this point of view provides an…
In this work, we show the convergence of adaptive lowest-order FEM (AFEM) for an elliptic obstacle problem with non-homogeneous Dirichlet data, where the obstacle \chi\ is restricted only by \chi\ in H^2(\Omega). The adaptive loop is…
We develop the a posteriori error analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…