Related papers: On the best accuracy using the $h$-adaptive finite…
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 propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
We consider linear inverse problems under white noise. These types of problems can be tackled with, e.g., iterative regularisation methods and the main challenge is to determine a suitable stopping index for the iteration. Convergence…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…
A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
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 this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…
We design and analyze an adaptive $hp$-finite element method (hp-AFEM) in dimensions $n=1,2$. The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best $hp$-approximation of the current discrete solution and data to a…
We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk Sampling-based algorithm from a given continuous density…
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…
Full interpretation of data from gravitational wave observations will require accurate numerical simulations of source systems, particularly binary black hole mergers. A leading approach to improving accuracy in numerical relativity…