Related papers: Semi-Lagrangian methods for parabolic problems in …
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coefficients. A generalized Cordes condition is imposed to…
We solve an inverse problem for fluid particle pair-statistics: we show that a time sequence of probability density functions (PDF's) of separations can be exactly reproduced by solving the diffusion equation with a suitable time-dependent…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
We develop a third-order conservative semi-Lagrangian discontinuous Galerkin (SLDG) scheme for solving linear transport equations on curvilinear unstructured triangular meshes, tailored for complex geometries. To ensure third-order spatial…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
This study proposes and analyses a novel higher-order, structure preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The method is built on a multisymplectic variational principle discretized over a…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…