Error Control, Adaptive Discretizations, and Applications, Part 2

1st Edition, Volume 59 - October 31, 2024
Imprint: Academic Press
Editors: Franz Chouly, Stéphane P.A. Bordas, Roland becker, Pascal Omnes
Language: English
Hardback ISBN:
9 7 8 - 0 - 4 4 3 - 2 9 4 5 0 - 1
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 2 9 4 5 1 - 8

Error Control, Adaptive Discretizations, and Applications, Volume 59, Part Two highlights new advances in the field, with this new volume presenting interesting chapters writte… Read more

Error Control, Adaptive Discretizations, and Applications, Part 2

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Error Control, Adaptive Discretizations, and Applications, Volume 59, Part Two highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems,

An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations.

Title of Book
Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
Chapter One: Anisotropic adaptive finite elements for aluminium electrolysis
Abstract
1 Introduction
2 A fluid flow problem arising from aluminium electrolysis
3 An error indicator for finite elements with large aspect ratio
4 An anisotropic, adaptive algorithm
5 Anisotropic adapted meshes
6 Interface update and final results on adapted meshes
Acknowledgements
References
Chapter Two: A posteriori single- and multi-goal error control and adaptivity for partial differential equations
Abstract
1 Introduction
2 Notation, abstract setting, finite element discretization
3 Single-goal oriented error control
4 Error estimation for non-standard discretizations
5 Multi-goal oriented error control
6 Applications
7 Conclusions and outlook
Acknowledgments
References
Chapter Three: Parameter optimization for elliptic-parabolic systems by an adaptive trust-region reduced basis method
Abstract
1 Introduction
2 The coupled elliptic-parabolic PDE
3 The discretization
4 Hierarchical a-posteriori error estimate for the state equation
5 The parameter optimization
6 Conclusions
References
Chapter Four: Iterative solvers in adaptive FEM: Adaptivity yields quasi-optimal computational runtime
Abstract
1 Motivation
2 Adaptive mesh-refining algorithm
3 Numerical experiments
4 Convergence analysis
5 Extension 1: Goal-oriented adaptivity
6 Extension 2: Non-symmetric problems
7 Extension 3: Non-linear problems
8 Further generalizations and comments
Acknowledgments
References
Chapter Five: Extending h adaptivity with refinement patterns
Abstract
1 Introduction
2 Mathematical description
3 Data structure and implementation aspects
4 Refinement pattern tools
5 Refinement pattern database
6 Examples
7 Conclusions
8 Extensions and future work
Acknowledgments
References
Chapter Six: On the accuracy and efficiency of reduced order models: Towards real-world applications
Abstract
1 Introduction
2 Reduced order models
3 Test cases
4 Argos and atlas
5 Conclusions
Ackwnoledgments
References
Chapter Seven: A posteriori error control and mesh adaptation for turbulence
Abstract
1 Introduction
2 CFD and the need for mesh adaptation
3 Anatomy of turbulent flow
4 Computational models and numerical methods
5 Boundary conditions
6 A posteriori error estimation
7 Summary
Acknowledgments
References
Chapter Eight: Model verification, updating, and selection from the constitutive relation error concept
Abstract
1 Introduction
2 Model verification with the CRE concept
3 Goal-oriented error estimation with the CRE concept
4 Model updating with the CRE concept
5 Model selection with the CRE concept
Funding & acknowledgments
References

Franz Chouly

Franz Chouly is professor at the University of Burgundy (Dijon, France). His research is focused on the numerical analysis of partial differential equations and variational inequalities, finite element methods, and applications in fluid and solid mechanics.

Affiliations and expertise

Professor, University of Burgundy, Dijon, France

Stéphane P.A. Bordas

Stéphane is a multi-disciplinary computational and data science researcher, educator, mentor and coach. He was trained as an engineer and applied mathematician who has been teaching and researching in computational sciences since year 1999, in various capacities. He has been in the top 1% most cited in his field, worldwide since year 2015 (ISI Clarivate). Stéphane leads the Legato Team (legato-team.eu), a multi-disciplinary team of about 30 researchers of a dozen nationalities. He is focusing on bringing the rigour of mathematics to bring intuition into the behaviour of complex systems. In particular, he pioneered new approaches to guarantee the quality of surgical simulation devices. The philosophy that he has been following is to create methodologies which translate across discipline boundaries. For example, the methodological backbone of his PhD thesis supports applications in fracture mechanics, nanoscale heterogeneities, biofilm growth, cancer growth, astrocytic metabolism and many others. Recently, his team has become involved, through the Institute of Advanced Studies of the University of Luxembourg in the nascent field of Computational Archaeology. Currently, one of the main focus points of his Team is to bring machine learning tools to bear on mathematical models of physical phenomena. In particular, his group develops adaptive data assimilation, model selection and discretisation optimisation schemes for the deformation of soft matter under large deformation with applications to surgical simulations and robotics. His team has been applying such ideas to programmable matter, multi-scale material modelling, wind energy harvesting, chemical engineering process optimisation, among others. Stéphane has taught over 5,000 students directly and given short courses and research seminars reaching thousands of attendees. He has extensive experience in one-to-one tutoring, mentoring and coaching across various disciplines. He has directly worked with over four hundred collaborators and over fifty different companies, worldwide, as an R&D consultant. Stéphane and his students and collaborators received multiple international prizes for their research and mentorship. He has raised over 28 million euros in research funding from the private and public sector alike. He is Fellow of the Learned Society of Wales, and recipient of the 2022 Eugenio Beltrami Senior Scientist Prize. He is Editor in Chief of Advances in Applied Mechanics, Executive Editor of Data-Centric Engineering, and Subject Editor for Applied Mathematical Modelling.

Affiliations and expertise

Research Unit in Eng Science, University of Luxembourg, Luxembourg

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