Formulation and Analysis of a Parameter-Free Stabilized Finite Element Method

DOI10.1137/14096284XzbMath1326.65159OpenAlexW2146372253MaRDI QIDQ3196608

Mauro Perego, Pavel B. Bochev, Kara J. Peterson

Publication date: 30 October 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/14096284x

zbMATH Keywords

finite elementsstabilizationadvection-diffusionedge elementsnumerical studiesScharfetter-Gummel upwinding

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

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• A parameter-free stabilized finite element method for scalar advection-diffusion problems
• A new control volume finite element method for the stable and accurate solution of the drift-diffusion equations on general unstructured grids
• On the definition of the SUPG parameter
• A new finite element formulation for computational fluid dynamics. II. Beyond SUPG
• Mixed finite elements in \(\mathbb{R}^3\)
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• What are \(C\) and \(h\)?: Inequalities for the analysis and design of finite element methods
• A multiscale finite element method for elliptic problems in composite materials and porous media
• Theory and practice of finite elements.
• Comparison of some finite element methods for solving the diffusion-convection-reaction equation
• Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Enhanced RFB method
• A stabilized formulation for the advection-diffusion equation using the Generalized Finite Element Method
• Finite element exterior calculus, homological techniques, and applications
• Enhanced residual‐free bubble method for convection–diffusion problems
• Convergence Analysis of a Multiscale Finite Element Method for Singularly Perturbed Problems

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