We present an efficient implementation of the double adaptivity algorithm Cohen et al. (2012) within setting Petrov–Galerkin method with optimal test functions. apply this to ultraweak variational formulation a general linear problem discretized standard Galerkin finite element method. As example, we demonstrate feasibility in context convection-dominated diffusion problem. The presented ideas,...

We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving p...

In this paper we investigate the numerical approximation of fractional diffusion, advection, reaction equation on a bounded interval. Recently explicit form solution to was obtained. Using boundary behavior and Jacobi polynomials, Petrov–Galerkin scheme is proposed analyzed. Numerical experiments are presented which support theoretical results, demonstrate accuracy optimal convergence method.

Starting from the generalized Lax-Milgram theorem and from the fact that the approximation error is minimized when the continuity and inf– sup constants are unity, we develop a theory that provably delivers well-posed approximation methods with unity continuity and inf–sup constants for numerical solution of linear partial differential equations. We demonstrate our single-framework theory on sc...