A convergence result for an iterative method for the equations of a stationary quasi-newtonian flow with temperature dependent viscosity
A convergent adaptive finite element method with optimal complexity.
A Convergent Finite Elemet Formulation for Transonic Flow.
A difference method for a nonlinear system of elliptic equations with mixed derivatives
A difference scheme for an elliptic system of nonlinear differential-functional equations with Dirichlet type boundary conditions. The existence and uniqueness of solution
A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines
For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...
A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms.
A discrete maximum principle [Book]
A Discrete Sampling Inversion Scheme for the Heat Equation.
A Discrete Solenoidal Finite Difference Scheme for the Numerical Approximation of Incompressible Flows.
A dissipative Galerkin method applied to some quasilinear hyperbolic equations
A domain decomposition algorithm for elliptic problems in three dimensions.
A domain decomposition analysis for a two-scale linear transport problem
We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating...
A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem
We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a non-diffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating...
A domain embedding method for Dirichlet problems in arbitrary space dimension
A dual mesh method for a nonlocal thermistor problem.
A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem
We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and polymeric components of the extra-stress tensor, as well...
A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity∗
We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k ≥ 1 for the approximation of the displacement field, and of order k or k − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields...
A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity
We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k ≥ 1 for the approximation of the displacement field, and of order k or k − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in both cases, with error estimates that are independent...