相关论文: Well-posedness and Robust Preconditioners for the …
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
A fundamental open problem in fluid dynamics is whether solutions to $2$D Euler equations with $(L^1_x\cap L^p_x)$-valued vorticity are unique, for some $p\in [1,\infty)$. A related question, more probabilistic in flavour, is whether one…
A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…
The Onsager-Stefan-Maxwell (OSM) equations are an important model of mass transport in multicomponent flows with multiple chemical species. They describe the coupling of diffusive fluxes between species, accounting for their interactions…
In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid-structure interaction with stochastic noise. We focus on a benchmark problem in stochastic fluid-structure interaction, and prove…
We establish local-in-time and global in time well-posedness for small data, for a coupled system of nonlinear acoustic structure interactions. The model consists of the nonlinear Westervelt equation on a bounded domain with non homogeneous…
Using the framework of operator or Cald\'{e}ron preconditioning, uniform preconditioners are constructed for elliptic operators of order $2s \in [0,2]$ discretized with continuous finite (or boundary) elements. The cost of the…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the…
We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the…
The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy…
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…
This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in $H^s, s>\frac{d}{2}+1$, the…
This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…