Related papers: Adaptive Uzawa algorithm for the Stokes equation
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…
The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We…
In this article, we discuss several classes of Uzawa smoothers for the application in multigrid methods in the context of saddle point problems. Beside commonly used variants, such as the inexact and block factorization version, we also…
In this paper, we propose and develop an optimal nonconforming finite element method for the Stokes equations approximated by the Crouzix-Raviart element for velocity and the continuous linear element for pressure. Previous result in using…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
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…
We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element…
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2d cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We…
In this report, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. First we present a first order ${\theta}$-scheme with the variable time step which is one parameter family of Linear Multi-step methods and…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…
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 this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…