相关论文: Nonstandard finite element de Rham complexes on cu…
We introduce a new variant of Nodal Virtual Element spaces that mimics the "Serendipity Finite Element Methods" (whose most popular example is the 8-node quadrilateral) and allows to reduce (often in a significant way) the number of…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
The structural degrees of freedom of a material are the various distortions most straightforwardly activated by external stimuli. A highly successful design strategy in materials chemistry involves controlling these individual distortions…
Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements in three dimensions are derived through a non-overlapping…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified N\'ed\'elec-Raviart-Thomas finite element methods for model problems in $\mathbf{H}(\operatorname{\mathbf{curl}})$ and…
We apply the well-established theoretical method developed for geometrical nonlinearities of micro/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
We consider new degrees of freedom for higher order differential forms on cubical meshes. The approach is inspired by the idea of Rapetti and Bossavit to define higher order Whitney forms and their degrees of freedom using small simplices.…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…
In this paper we describe generic algorithms and data structures for the implementation of $hp$-adaptive discontinuous finite element methods in the Dune-Fem library. Special attention is given to the often tedious and error-prone task of…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Standard nodal finite elements in electromagnetic analysis have well-known limitation of occurrence of spurious solution. In order to circumvent the problem, a penalty function method or a regularization method is used with potential…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…