Related papers: Preserving the accuracy of numerical methods discr…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…
We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main…
We develop a discretisation of the semigeostrophic rotating shallow water equations, based upon their optimal transport formulation. This takes the form of a Moreau-Yoshida regularisation of the Wasserstein metric. Solutions of the optimal…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
We present two efficient numerical methods for susceptibility artifact correction applicable in Echo Planar Imaging (EPI), an ultra fast Magnetic Resonance Imaging (MRI) technique widely used in clinical applications. Both methods address a…
In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained using symmetrization techniques.
In this work, we consider pressurized phase-field fracture problems in nearly and fully incompressible materials. To this end, a mixed form for the solid equations is proposed. To enhance the accuracy of the spatial discretization, a…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…