Related papers: An Adaptive Finite Element Method Based on General…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…
In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…
In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linear kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is…
In this work, we propose and analyze a pointwise a posteriori error estimator for simple eigenvalues of elliptic eigenvalue problems with adaptive finite element methods (AFEMs). We prove the reliability and efficiency of the residual-type…
Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
In our work, we consider the classical density-based approach to the topology optimization. We propose to modify the discretized cost functional using a posteriori error estimator for the finite element method. It can be regarded as a new…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization…
In this paper, we study the "a posteriori" error estimate corresponding to the Brinkman-Darcy-Forchheimer problem. We introduce the variational formulation discretised by using the finite element method. Then, we establish an "a posteriori"…
We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress…
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schr\"odinger-type equations, in the $L^\infty(L^2)-$norm. For the discretization in time we use the Crank-Nicolson method, while for the space…
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…