Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems

Alexandre Ern; Iain Smears; Martin Vohralík

doi:10.1137/16m1097626

Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/16m1097626 ◽

2017 ◽

Vol 55 (6) ◽

pp. 2811-2834 ◽

Cited By ~ 12

Author(s):

Alexandre Ern ◽

Iain Smears ◽

Martin Vohralík

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Space Time ◽

High Order ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Polynomial Degree

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A Posteriori Error Estimates for Higher Order Space-Time Galerkin Discretizations of Nonlinear Parabolic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/18m117594x ◽

2021 ◽

Vol 59 (3) ◽

pp. 1486-1509

Author(s):

Vít Dolejší ◽

Filip Roskovec ◽

Miloslav Vlasák

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Higher Order ◽

Space Time ◽

Parabolic Problems ◽

A Posteriori ◽

Nonlinear Parabolic Problems ◽

A Posteriori Error ◽

Nonlinear Parabolic

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Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems

Numerical Mathematics and Advanced Applications ◽

10.1007/978-3-540-34288-5_8 ◽

2007 ◽

pp. 135-150

Author(s):

Sergey Repin

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Functional Approach ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error

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$hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems

SIAM Journal on Scientific Computing ◽

10.1137/15m1026687 ◽

2016 ◽

Vol 38 (5) ◽

pp. A3220-A3246 ◽

Cited By ~ 18

Author(s):

Vít Dolejší ◽

Alexandre Ern ◽

Martin Vohralík

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Elliptic Problems ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Polynomial Degree

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A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/070708792 ◽

2009 ◽

Vol 47 (3) ◽

pp. 2157-2176 ◽

Cited By ~ 21

Author(s):

Alan Demlow ◽

Omar Lakkis ◽

Charalambos Makridakis

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Maximum Norm ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error

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A Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Parabolic Problems Coupled through a Boundary

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/140964059 ◽

2015 ◽

Vol 3 (1) ◽

pp. 169-198 ◽

Cited By ~ 8

Author(s):

T. Arbogast ◽

D. Estep ◽

B. Sheehan ◽

S. Tavener

Keyword(s):

Finite Element ◽

Error Estimates ◽

Finite Volume ◽

Mixed Finite Element ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Finite Volume Methods ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error

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A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces

Numerische Mathematik ◽

10.1007/s00211-008-0165-7 ◽

2008 ◽

Vol 110 (3) ◽

pp. 257-275 ◽

Cited By ~ 3

Author(s):

E. Cuesta ◽

Ch. Makridakis

Keyword(s):

Banach Spaces ◽

Error Estimates ◽

Maximal Regularity ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Parabolic Problems ◽

A Posteriori ◽

Nonlinear Parabolic Problems ◽

A Posteriori Error ◽

Nonlinear Parabolic

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Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142902406314 ◽

2003 ◽

Vol 41 (4) ◽

pp. 1585-1594 ◽

Cited By ~ 83

Author(s):

Charalambos Makridakis ◽

Ricardo H. Nochetto

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Elliptic Reconstruction

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Sharply local pointwise a posteriori error estimates for parabolic problems

Mathematics of Computation ◽

10.1090/s0025-5718-10-02346-x ◽

2010 ◽

Vol 79 (271) ◽

pp. 1233-1262 ◽

Cited By ~ 3

Author(s):

Alan Demlow ◽

Charalambos Makridakis

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Parabolic Problems ◽

A Posteriori ◽

A Posteriori Error

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A Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2017.1338730 ◽

2017 ◽

Vol 38 (12) ◽

pp. 1527-1547

Author(s):

Jhuma Sen Gupta ◽

Rajen Kumar Sinha

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Parabolic Problems ◽

A Posteriori ◽

Lumped Mass ◽

A Posteriori Error ◽

Elliptic Reconstruction

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A posteriori error estimates for fully discrete nonlinear parabolic problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2007.03.015 ◽

2007 ◽

Vol 196 (35-36) ◽

pp. 3462-3474 ◽

Cited By ~ 10

Author(s):

Javier de Frutos ◽

Bosco García-Archilla ◽

Julia Novo

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Parabolic Problems ◽

A Posteriori ◽

Nonlinear Parabolic Problems ◽

A Posteriori Error ◽

Fully Discrete ◽

Nonlinear Parabolic

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