A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
Computer Methods in Applied Mechanics and Engineering
A consistent approximate upwind Petrov—Galerkin method for convection-dominated problems
Computer Methods in Applied Mechanics and Engineering
Finite element analysis of the compressible Euler and Navier-Stokes equations
Finite element analysis of the compressible Euler and Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Feedback Petrov-Galerkin methods for convection-dominated problems
Computer Methods in Applied Mechanics and Engineering
Stabilized finite element methods. I: Application to the advective-diffusive model
Computer Methods in Applied Mechanics and Engineering
A new approach to algorithms for convection problems which are based on exact transport + projection
Computer Methods in Applied Mechanics and Engineering
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Stabilized hp-Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Numerical Analysis
An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation
SIAM Journal on Numerical Analysis
A Generalization of the Local Projection Stabilization for Convection-Diffusion-Reaction Equations
SIAM Journal on Numerical Analysis
Stabilized fully-coupled finite elements for elastohydrodynamic lubrication problems
Advances in Engineering Software
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The numerical analysis of the CAU (Consistent Approximate Upwind) Petrov-Galerkin method of convection dominated reaction-diffusion problems is presented. The main issue in this analysis is that it considers elements with high interpolation orders and yields new definitions for the upwind functions and the local Peclet number in terms of the characteristic element h and the element interpolation order p. For regular solutions, the CAU method gets quasi-optimal convergence rate for the streamline derivative, keeping the same SUPG (Streamline Upwind Petrov-Galerkin) convergence rates. This improves the well-known h-version error analysis in [Comput. Methods Appl. Mech. Engrg. 45 (1984) 285] and the hp-version in [SIAM J. Numer. Anal. 37 (2000) 1618] for SUPG-like methods. It also improves the a priori analysis for shock-capturing methods presented in [Comput. Methods Appl. Mech. Engrg. 191 (2002) 2997].