Related papers: Cut Finite Element Methods for Partial Differentia…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the Laplace-Beltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can…
We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the…
We study cut finite element discretizations of a Darcy interface problem based on the mixed finite element pairs $\textbf{RT}_k\times Q_k$, $k\geq 0$. Here $Q_k$ is the space of discontinuous polynomial functions of degree less or equal to…
In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order…
The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
Numerical solutions of partial differential equations (PDEs) on manifolds continues to generate a lot of interest among scientists in the natural and applied sciences. On the other hand, recent developments of 3D scanning and computer…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
A family of quadratic finite volume method (FVM) schemes are constructed and analyzed over tetrahedral meshes. In order to prove stability and error estimate, we propose the minimum V-angle condition on tetrahedral meshes, and the surface…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming $C^1$-continuous finite elements. We implement the…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
Projection stabilisation applied to general Lagrange multiplier finite element methods is introduced and analysed in an abstract framework. We then consider some applications of the stabilised methods: (i) the weak imposition of boundary…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…