Related papers: Adaptive finite element method for an elliptic opt…
The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
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,…
This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
We propose a new and simpler residual based a posteriori error estimator for finite element approximation of the elliptic obstacle problem. The results in the article are two fold. Firstly, we address the influence of the inhomogeneous…
This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…
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…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…
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…
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…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
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, 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…
We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…
In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis…
We analyze a reliable and efficient max-norm a posteriori error estimator for a control-constrained, linear-quadratic optimal control problem. The estimator yields optimal experimental rates of convergence within an adaptive loop.