Related papers: On optimal finite element schemes for biharmonic e…
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…
We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…
This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
In this paper we derive a necessary condition for finite element method (FEM) convergence in $H^1(\Omega)$ as well as generalize known sufficient conditions. We deal with the piecewise linear conforming FEM on triangular meshes for…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…
Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…
We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element differential complex of lowest-order, known as the complex of…
In this study, two-dimensional finite element complexes with various levels of smoothness, including the de Rham complex, the curldiv complex, the elasticity complex, and the divdiv complex, are systematically constructed. Smooth scalar…
A nonconforming $P_3$ finite element is constructed by enriching the conforming $P_3$ finite element space with three $P_3$ nonconforming bubbles and six additional $P_4$ nonconforming bubbles, on each tetrahedron. Here the divergence of…
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…