Related papers: Finite element analysis of an eigenvalue problem a…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics. In…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…
The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms, such as those arizing from electromagnetic fields, we develop some abstract…
We present and analyze a weak Galerkin finite element method for solving the transport-reaction equation in $d$ space dimensions. This method is highly flexible by allowing the use of discontinuous finite element on general meshes…
A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport…
This article is devoted to computing the eigenvalue of the Laplace eigenvalue problem by the weak Galerkin (WG) finite element method with emphasis on obtaining lower bounds. The WG method is on the use of weak functions and their weak…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…