Dual-baseda posteriorierror estimate for stochastic finite element methods

Dual-based a Posteriori Error Estimate for Stochastic Finite Element Methods

Posteriorierror Estimator for the Finite Element Methodwith Super Convergence

When the nite element solution of a variational problem possesses certain super convergence properties, it is possible very inexpensively to obtain a correction term providing an additional order of approximation of the solution. The correction can be used for error estimation locally or globally in whatever norm is preferred, or if no error estimation is wanted it can be used for postprocessin...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Dual Formulations of Mixed Finite Element Methods

Abstract Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge ...

Parallel Stochastic Dynamic Programming: Finite Element Methods

A finite element method for stochastic dynamic programming is developed. The computational method is valid for a general class of optimal control problems that are nonlinear and perturbed by general Markov noise in continuous time, including jump Poisson noise. Stability and convergence of the method are verified and its storage utilization efficiency over the traditional finite difference meth...