Related papers: Finite element discretization of non-linear diffus…
In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM) models in fractured porous media accounting for Coulomb frictional contact at matrix fracture interfaces. The simulation of such models plays an important role in…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We study non-equilibrium velocity fluctuations in a model for the sedimentation of non-Brownian particles experiencing long-range hydrodynamic interactions. The complex behavior of these fluctuations, the outcome of the collective dynamics…
We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology, which allows a direct coupling between…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
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…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the…
We propose an edge averaged finite element(EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of the computed charged density functions and temperature function. Also…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in…
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…
There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates…
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic particle methods are incompatible with diffusive partial…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…