Space‐time PU‐DWR error control and adaptivity for the heat equation

Thiele, Jan Philipp; Wick, Thomas

doi:10.1002/pamm.202100174

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2024

Publication Types

Select...

Other1

Book1

Article1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We demonstrate the performance in terms of error estimation and adaptivity [1], and optimal control [2] and some recent open-source documentation for the stationary case [3]. The presentation concludes with current developments and some preliminary findings of ongoing work [4].…”

mentioning

confidence: 93%

Space-time fluid-structure interaction: formulation and dG(0) time discretization

Khimin¹,

Roth²,

Wick³

2022

8th European Congress on Computational Methods in Applied Sciences and Engineering

View full text Add to dashboard Cite

mentioning

confidence: 93%

Space-time fluid-structure interaction: formulation and dG(0) time discretization

Khimin¹,

Roth²,

Wick³

2022

8th European Congress on Computational Methods in Applied Sciences and Engineering

View full text Add to dashboard Cite

Space-Time Error Control Using a Partition-of-Unity Dual-Weighted Residual Method Applied to Low Mach Number Combustion

Thiele

Wick

2022

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

Thiele,

Wick

2024

J Sci Comput

View full text Add to dashboard Cite

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples.

show abstract

Space‐time PU‐DWR error control and adaptivity for the heat equation

Abstract: In this work, space‐time goal‐oriented a posteriori error estimation using a partition‐of‐unity localization is applied to the linear heat equation. The algorithmic developments are substantiated with a numerical example.

Cited by 3 publications

References 5 publications

Space-time fluid-structure interaction: formulation and dG(0) time discretization

Space-time fluid-structure interaction: formulation and dG(0) time discretization

Space-Time Error Control Using a Partition-of-Unity Dual-Weighted Residual Method Applied to Low Mach Number Combustion

Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

Contact Info

Product

Resources

About