A computational domain decomposition approach for solving coupled flow-structure-thermal interaction problems.
A conforming finite element method with Lagrange multipliers for the biharmonic problem
A conservative particle approximation for a boundary advection-diffusion problem
A Constructive Method for Deriving Finite Elements of Nodal Type.
A continuous finite element method with face penalty to approximate Friedrichs' systems
A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number...
A convergent adaptive finite element method with optimal complexity.
A Convergent Finite Elemet Formulation for Transonic Flow.
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 dissipative Galerkin method applied to some quasilinear hyperbolic equations
A domain decomposition algorithm for elliptic problems in three dimensions.
A domain embedding method for Dirichlet problems in arbitrary space dimension
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...
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 Higher Order Mixed Finite Element Methods for Plane Elasticity.
A Family of Mixed Finite Elements for Linear Elasticity.
A Family of Mixed Finite Elements for the Elasticity Problem.
A Fast Iterative Method for Solving Stationary Heat Conduction Problems on Regions Partitioned into Rectangles.