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. 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.

• 1. Preface2. Selling’s decomposition and the anisotropic wave equationJean-Marie Mirebeau, Haloui Malik and Ludovic Metivier3. Chapter name yet to be determined.Michel Duprez and Franz Chouly4. Anisotropic recovery-based error estimators and mesh adaptation for real-life engineering innovationSimona Perotto, Erika Temellini, Nicola Ferro, Luca Liverotti and Giacomo Speroni5. Tree-based adaptive finite element methods for deformable image registrationRicardo Ruiz Baier and Nicolás Alejandro Barnafi Wittwer6. Residual error estimators for Coulomb frictional contactPatrick Hild, Rodolfo Araya and Franz Chouly7. Chapter name yet to be determined.Iain Smears8. Parallel simulation and adaptive mesh refinement for 3D elasto- static contact mechanics problems between deformable bodiesIsabelle Ramière and Frederic Charles Lebon9. Chapter name yet to be determined.Andrea Cangiani and Georgoulis H. Emmanuil10. Optimal adaptive implicit time steppingMichael Feischl11. A posteriori error analysis for Finite Element approximation of some groundwater models Part II: Richards equation and mixed finite elementZoubida Mghazli12. A posteriori error estimates and adaptivity for locally conservative methodsMartin Vohralik

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. 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.

• 1. Preface2. Selling’s decomposition and the anisotropic wave equationJean-Marie Mirebeau, Haloui Malik and Ludovic Metivier3. Chapter name yet to be determined.Michel Duprez and Franz Chouly4. Anisotropic recovery-based error estimators and mesh adaptation for real-life engineering innovationSimona Perotto, Erika Temellini, Nicola Ferro, Luca Liverotti and Giacomo Speroni5. Tree-based adaptive finite element methods for deformable image registrationRicardo Ruiz Baier and Nicolás Alejandro Barnafi Wittwer6. Residual error estimators for Coulomb frictional contactPatrick Hild, Rodolfo Araya and Franz Chouly7. Chapter name yet to be determined.Iain Smears8. Parallel simulation and adaptive mesh refinement for 3D elasto- static contact mechanics problems between deformable bodiesIsabelle Ramière and Frederic Charles Lebon9. Chapter name yet to be determined.Andrea Cangiani and Georgoulis H. Emmanuil10. Optimal adaptive implicit time steppingMichael Feischl11. A posteriori error analysis for Finite Element approximation of some groundwater models Part II: Richards equation and mixed finite elementZoubida Mghazli12. A posteriori error estimates and adaptivity for locally conservative methodsMartin Vohralik