Abstract In phase change simulations, material properties such as density, viscosity, or thermal conductivity may exhibit jump discontinuities, possibly of several orders magnitude. These discontinuities represent interfaces between the phases, and they emerge naturally during simulation; thus, their exact location is generally unknown a priori. Our goal to simulate processes with meshfree gene...

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis based on variational techniques particular gradient flows space probability measures equipped distance arising Monge–Kantorovich optimal transport problem. The associated internal energy functionals gene...

Linear systems with very large off-diagonal elements and discontinuous coefficients (LODC systems) arise in some modeling cases, such as those involving heterogeneous media. Such problems are usually solved by domain decomposition methods, but these can be difficult to implement on unstructured grids or when the boundaries between subdomains have a complicated geometry. Gordon and Gordon have s...

In this paper we are interested in the well-posedness of a class of fully coupled forward-backward SDE (FBSDE) in which the forward drift coefficient is allowed to be discontinuous with respect to the backward component of the solution. Such an FBSDE is motivated by a practical issue in regime-switching term structure interest rate models, and the discontinuity makes it beyond any existing fram...

We study the problem of estimating the size of an inclusion embedded inside a two dimensional body with discontinuous conductivity by one voltage-current measurement. This problem is practically important because the conductivity of a human body is discontinuous. The proofs rely on quantitative uniqueness estimates for the conductivity equation with discontinuous coefficients.

A discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest Ω is assumed to be a union of polygonal substructures Ωi of size O(Hi). We allow this substructure decomposition to be geometrically nonconforming. Inside each substructure Ωi, a conforming finite element space associated to a triangulation Thi...

We propose a robust interpolation scheme for non-overlapping two-level domain decomposition methods applied to two-dimensional elliptic problems with discontinuous coefficients. This interpolation is used to design a preconditioner closely related to the BPS scheme proposed in [1]. Through numerical experiments, we show on structured and unstructured finite element problems that the new precond...