Related papers: Numerical Solution of the Two-Phase Obstacle Probl…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
We prove an existence and uniqueness result for the obstacle problem for quasilinear stochastic integral-partial differential equations. Our method is based on the probabilistic interpretation of the solution using backward doubly SDEs with…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The…
We consider the Serre system of equations which is a nonlinear dispersive system that models two-way propagation of long waves of not necessarily small amplitude on the surface of an ideal fluid in a channel. We discretize in space the…
Several important problems in partial differential equations can be formulated as integral equations. Often the integral operator defines the solution of an elliptic problem with specified jump conditions at an interface. In principle the…
We develop two-scale methods for computing the convex envelope of a continuous function over a convex domain in any dimension.This hinges on a fully nonlinear obstacle formulation [A. M. Oberman, "The convex envelope is the solution of a…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…
We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…