Related papers: Mean conservation for density estimation via diffu…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space.…
This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fr\'echet mean which often requires finding minimizing geodesics to each data point for each step of an iterative…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two dimensions (2D). We first present a…
A lack of regularity in the solution of the porous medium equation poses a serious challenge in its theoretical and numerical studies. A common strategy in theoretical studies is to utilize the pressure formulation of the equation where a…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…