Related papers: Report: Error estimation of recovered solution in …
We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the $p$-robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ…
This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation $u_t+\De\bigl(\eps \De u-\eps^{-1} f(u)\bigr)=0$. It is shown that the {\it…
Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…
In this paper, we develop a novel framework to optimally design spectral estimators for phase retrieval given measurements realized from an arbitrary model. We begin by deconstructing spectral methods, and identify the fundamental…
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element…
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…
Score matching estimators have garnered significant attention in recent years because they eliminate the need to compute normalizing constants, thereby mitigating the computational challenges associated with maximum likelihood estimation…
An explicit and computable error estimator for the $hp$ version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide $hp$…
The 2D/1D multiscale finite element method (MSFEM) is an efficient way to simulate rotating machines in which each iron sheet is exposed to the same field. It allows the reduction of the three dimensional sheet to a two dimensional…
The recent work [Kurz et al., Numer. Math., 147 (2021)] proposed functional a posteriori error estimates for boundary element methods (BEMs) together with a related adaptive mesh-refinement strategy. Unlike most a posteriori BEM error…
In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…
Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…
Sampling from Diffusion Models can alternatively be seen as solving differential equations, where there is a challenge in balancing speed and image visual quality. ODE-based samplers offer rapid sampling time but reach a performance limit,…
Sensitivity-based Finite Element Model Updating (FEMU) is one of the widely accepted techniques used for damage identification in structures. FEMU can be formulated as a numerical optimization problem and solved iteratively making automatic…
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…
Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…