Related papers: Analysis of the diffuse domain approach for a bulk…
In "I. Smears, E. S\"{u}li, \emph{Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cord\'{e}s coefficients. SIAM J. Numer Anal., 51(4):2088-2106, 2013}" the authors designed and analysed a…
In this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion , non-uniform advection and variably influencing reaction terms on Lipschitz continuous…
We introduce the notion of \delta-viscosity solutions for fully nonlinear uniformly parabolic PDE on bounded domains. We prove that \delta-viscosity solutions are uniformly close to the actual viscosity solution. As a consequence we obtain…
We consider the situation when an elliptic problem in a subdomain $\Omega_1$ of an $n$-dimensional bounded domain $\Omega$ is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in $\Omega\setminus\Omega_1$.…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the domain motion is implicit to the problem. We consider a…
In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph (BJ) interface conditions. Three Robin-type boundary conditions and a modified weak…
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…
In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet and / or no-flux…
We propose a two-point flux approximation finite-volume scheme for the approximation of two cross-diffusion systems coupled by a free interface to account for vapor deposition. The moving interface is addressed with a cut-cell approach,…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…
In the present work, we consider weakly-singular integral equations arising from linear second-order strongly-elliptic PDE systems with constant coefficients, including, e.g., linear elasticity. We introduce a general framework for optimal…
We prove convergence for the nonoverlapping Robin-Robin method applied to nonlinear elliptic equations with a $p$-structure, including degenerate diffusion equations governed by the $p$-Laplacian. This nonoverlapping domain decomposition is…
Considering fractional fast diffusion equations on bounded open polyhedral domains in $\mathbb{R}^N$, we give a fully Galerkin approximation of the solutions by $C^0$-piecewise linear finite elements in space and backward Euler…
In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
We present a numerical framework to approximate the $\mu$-domain in the planar Skorokhod embedding problem (PSEP), recently appeared in \cite{gross2019}. Our approach investigates the continuity and convergence properties of the solutions…
In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…