Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.200410101 ◽

2004 ◽

Vol 84 (1) ◽

pp. 3-21 ◽

Author(s):

C. Carstensen

Keyword(s):

Finite Element ◽

Error Analysis ◽

A Posteriori ◽

Element Error ◽

Averaging Techniques

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A tutorial in elementary finite element error analysis: A systematic presentation of a priori and a posteriori error estimates

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(97)00230-2 ◽

1998 ◽

Vol 158 (1-2) ◽

pp. 1-22 ◽

Author(s):

James R Stewart ◽

Thomas J.R Hughes

Keyword(s):

Finite Element ◽

Error Analysis ◽

Error Estimates ◽

A Priori ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

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Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis

Numerische Mathematik ◽

10.1007/s00211-004-0548-3 ◽

2004 ◽

Vol 99 (1) ◽

pp. 1-24 ◽

Author(s):

S. Bartels ◽

C. Carstensen ◽

G. Dolzmann

Keyword(s):

Finite Element ◽

Error Analysis ◽

A Priori ◽

A Posteriori ◽

Dirichlet Conditions ◽

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Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.3104 ◽

2014 ◽

Vol 38 (4) ◽

pp. 738-750 ◽

Author(s):

Emmanuel Creusé ◽

Serge Nicaise ◽

Zuqi Tang

Keyword(s):

Finite Element ◽

Error Analysis ◽

Boundary Conditions ◽

Vector Fields ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Helmholtz Decomposition ◽

Maxwell System ◽

A Posteriori ◽

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A Posteriori Finite Element Error Analysis for Symmetric Positive Differential Equations

Numerical Functional Analysis and Optimization ◽

10.1080/01630569908816906 ◽

1999 ◽

Vol 20 (5-6) ◽

pp. 473-490 ◽

Author(s):

Jang Jou ◽

Jinn-Liang Liu

Keyword(s):

Finite Element ◽

Differential Equations ◽

Error Analysis ◽

A Posteriori ◽

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An a posteriori finite element error analysis for the stokes equations

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(99)00271-x ◽

2000 ◽

Vol 114 (2) ◽

pp. 333-343 ◽

Author(s):

Jang Jou ◽

Jinn-Liang Liu

Keyword(s):

Finite Element ◽

Error Analysis ◽

Stokes Equations ◽

A Posteriori ◽

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Averaging techniques for reliable and efficient a posteriori finite element error control: analysis and applications

Recent Advances in Adaptive Computation - Contemporary Mathematics ◽

10.1090/conm/383/07155 ◽

2005 ◽

pp. 15-34 ◽

Author(s):

Carsten Carstensen ◽

Max Jensen

Keyword(s):

Finite Element ◽

Error Control ◽

Control Analysis ◽

A Posteriori ◽

Element Error ◽

Averaging Techniques

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Averaging techniques yield reliable a posteriori finite element error control for obstacle problems

Numerische Mathematik ◽

10.1007/s00211-004-0553-6 ◽

2004 ◽

Vol 99 (2) ◽

pp. 225-249 ◽

Author(s):

S. Bartels ◽

C. Carstensen

Keyword(s):

Finite Element ◽

Error Control ◽

Obstacle Problems ◽

A Posteriori ◽

Element Error ◽

Averaging Techniques

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All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable

Mathematics of Computation ◽

10.1090/s0025-5718-03-01580-1 ◽

2003 ◽

Vol 73 (247) ◽

pp. 1153-1166 ◽

Author(s):

C. Carstensen

Keyword(s):

Finite Element ◽

Error Control ◽

Unstructured Grids ◽

A Posteriori ◽

First Order ◽

Element Error ◽

Averaging Techniques

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A Posteriori Least-Squares Finite Element Error Analysis for the Navier–Stokes Equations

Numerical Functional Analysis and Optimization ◽

10.1081/nfa-120020245 ◽

2003 ◽

Vol 24 (1-2) ◽

pp. 67-74 ◽

Author(s):

Jang Jou ◽

Jinn-Liang Liu

Keyword(s):

Finite Element ◽

Error Analysis ◽

Least Squares ◽

Stokes Equations ◽

Navier Stokes ◽

A Posteriori ◽

Navier Stokes Equations ◽

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The norm of a discretized gradient in $$\varvec{H({{\mathrm{div}}})^*}$$ H ( div ) ∗ for a posteriori finite element error analysis

Numerische Mathematik ◽

10.1007/s00211-015-0728-3 ◽

2015 ◽

Vol 132 (3) ◽

pp. 519-539 ◽

Author(s):

Carsten Carstensen ◽

Daniel Peterseim ◽

Andreas Schröder

Keyword(s):

Finite Element ◽

Error Analysis ◽

A Posteriori ◽

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