Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems

Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems

We derive local error estimates for the discretization of optimal control problems governed by linear advection-diffusion partial differential equations (PDEs) using the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method. We show that if the SUPG method is used to solve optimization problems governed by an advection-dominated PDE the convergence properties of the SUPG met...

Residual-free bubbles for advection-diffusion problems: the general error analysis

We develop the general a priori error analysis of residual-free bubble nite element approximations to non-self-adjoint elliptic problems of the form ("A+C)u = f subject to homogeneous Dirichlet boundary condition, where A is a symmetric second-order elliptic operator, C is a skew-symmetric rst-order diierential operator, and " is a positive parameter. Optimal-order error bounds are derived in v...

A robust a posteriori estimator for the Residual-free Bubbles method applied to advection-diffusion problems

Coupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material

This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin met...

A Simplified Solution for Advection Dominated Accretion Flows with Outflow

The existence of outflow in the advection dominated accretion flows has been confirmed by both numerical simulations and observations. The outow models for ADAF have been investigated by several groups with a simple self similar solution. But this solution is inaccurate at the inner regions and can not explain the emitted spectrum of the flow; so, it is necessary to obtain a global solution for...