相关论文: Instance optimal Crouzeix-Raviart adaptive finite …
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
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…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
We prove new optimality results for adaptive mesh refinement algorithms for non-symmetric, indefinite, and time-dependent problems by proposing a generalization of quasi-orthogonality which follows directly from the inf-sup stability of the…
In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the…
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
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 article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Adaptive mesh refinement (AMR) is indispensable for efficient finite element analyses. However, its performance depends not only on the refinement itself but also on strategy to mark elements for refinement and the way it is tuned. This…
The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they…
In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…
The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain $\Omega \subset \mathbb R^N \, (N=2,3)$. We propose a finite element scheme based on the nonconforming P1/P0 approximation…
We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider…
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
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…
We consider the solution of second order elliptic PDEs in $\R^d$ with inhomogeneous Dirichlet data by means of an $h$-adaptive FEM with fixed polynomial order $p\in\N$. As model example serves the Poisson equation with mixed…
We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…