Degenerate stationary problems with homogeneous boundary conditions.
Derivation of high-order spectral methods for time-dependent PDE using modified moments.
Difference methods for non-linear partial differential equations of the first order
Difference methods for parabolic functional differential problems of the Neumann type
Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions...
Difference schemes with nonlocal boundary conditions.
Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions
The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation...
Discontinuous solutions of the Cauchy problems for a scalar equation in nonconservative form
Discrete maximum principle in parabolic boundary-value problems
Discretizing a backward stochastic differential equation.
Dual-mixed finite element methods for the Navier-Stokes equations
A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.