相关论文: A Nonconforming Finite Element Approximation for t…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials ($P_3$) and possesses $\mathcal{O}(h^2)$ convergence rate in energy norm on general shape-regular…
We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our…
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…
In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…
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…
We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both theoretical and practical senses. Since various error constants must be quantitatively evaluated for…
A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on $P_1\times…
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is…
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the…
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…