Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with and coefficients.
Regions of Stability, Equivalence Theorems and the Courant-Friedrichs-Lewy Condition.
Relaxation models of phase transition flows
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
Resolvent estimates in for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes.
Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces.
Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
Roe Scheme for Two-layer Shallow Water Equations: Application to the Strait of Gibraltar
The flow trough the Strait of Gibraltar could be analyzed as a problem of two-layer hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The shallow water equations in both layers coupled together are an important tool to simulate this phenomenon. In this paper we perform an upwind schemes for hyperbolic equations based on the Roe approximate Riemann solver, to study the resulting model. The main goal assigned was to predict the location of the interface between the two layers....
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Runge-Kutta methods for parabolic equations with nonsmooth initial data