Related papers: Convergence of the adaptive finite element discret…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
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…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
In this paper we discuss the optimal convergence of a standard adaptive scheme based on mixed finite element approximation to the solution of the eigenvalue problem associated with the Stokes equations. The proofs of the quasi-orthogonality…
This paper presents a strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
The a posteriori error analysis of the classical Argyris finite element methods dates back to 1996, while the optimal convergence rates of associated adaptive finite element schemes are established only very recently in 2021. It took a long…
A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is…
We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…
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…
In this paper we study finite element discretizations of a surface vector-Laplace eigenproblem. We consider two known classes of finite element methods, namely one based on a vector analogon of the Dziuk-Elliott surface finite element…
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…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…
In this paper, we propose and analyze a mixed virtual element method for the approximation of the eigenvalues and eigenfunctions of the two-dimensional elasticity eigenvalue problem. Under standard assumptions on polygonal meshes, we prove…
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…