Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important open problems in th...

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Published inComputing and visualization in science Vol. 19; no. 5-6; pp. 47 - 63
Main Authors John, Volker, Knobloch, Petr, Novo, Julia
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 15.12.2018
Springer Nature B.V
Subjects
Algorithms
Calculus of Variations and Optimal Control; Optimization
Computational fluid dynamics
Computational Mathematics and Numerical Analysis
Computer Applications in Chemistry
Convection
Finite element method
Fluid flow
Incompressible flow
Mathematics
Mathematics and Statistics
Numerical Analysis
Special Issue FEM Symposium 2017
Visualization
SUPG Method
Posteriori Error Estimators
Finite Element Error Analysis
Incompressible Flow Problems
Time-dependent Navier-Stokes Equations
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Summary:The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important open problems in these fields are discussed. The exposition concentrates on H 1 -conforming finite elements.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-018-0290-5