Related papers: A General Superapproximation Result
For some class of mappings, which are generalization of space quasiisometries, an upper estimate for a measure of image of a ball is obtained. As consequence, it is obtained one analog of Schwartz lemma for mappings mentioned above. Results…
We rewrite the standard nodal virtual element method as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally reconstructing broken fluxes and potentials on elemental…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
In this paper, we present finite element approximations of a class of Generalized random fields defined over a bounded domain of R d or a smooth d-dimensional Riemannian manifold (d $\ge$ 1). An explicit expression for the covariance matrix…
Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online…
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [21] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
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…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
In this paper we provide some error estimates for the div least-squares finite element method on elliptic problems. The main contribution is presenting a complete error analysis, which improves the current \emph{state-of-the-art} results.…
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…
In transferring some results from universal Taylor series to the case of Pad\'e approximants we obtain stronger results, such as, universal approximation on compact sets of arbitrary connectivity and generic results on planar domains of any…
In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…
We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by…