Related papers: A General Superapproximation Result
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower…
In this paper, we analyze how global optima of an agent's preferences can be reconstructed from the solutions found for local problems. A sheaf-theoretic analysis provides an abstract characterization of the global solution, and polynomial…
This document gives guidelines to set up, run, and postprocess correct simulations with the finite element method. It is not an introduction to the method itself, but rather a list of things to check and possible mistakes to watch out for…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…
The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble-Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative…
In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equation under minimal regularity assumptions on general…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
This paper presents a new mixed finite element method for the Cahn-Hilliard equation. The well-posedness of the mixed formulation is established and the error estimates for its linearized fully discrete scheme are provided. The new mixed…
This paper considers the use of singular perturbation approximations for general linear quantum systems where the system dynamics are described in terms of both annihilation and creation operators. Results that are related to the physical…
The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations…
We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such…
We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to…
The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of…