Related papers: Adaptive Uzawa algorithm for the Stokes equation
In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Navier-Stokes equations corresponding to given measurements on…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…
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 work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of the energy error and the oscillation. This result will be…
The Stokes-Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the…
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…
Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…
The emergence of deep learning has stimulated a new class of PDE solvers in which the unknown solution is represented by a neural network. Within this framework, residual minimization in dual norms -- central to weak adversarial neural…