Dr. Mihai **Nechita**

### Current position:

Researcher at *Tiberiu Popoviciu Institute of Numerical Analysis*

Previously, I did my Phd at *University College London* and a postdoc at *Inria Paris (team Commedia)*

### Interests:

- Numerical Analysis
- Finite Element Methods
- Partial Differential Equations
- Inverse Problems
- Scientific Computing

- New paper: E. Burman, M. Nechita, L. Oksanen,
*Optimal finite element approximation of unique continuation*, arXiv 2311.07440 (2023). - Gave a talk in the workshop Simulation of data assimilation under PDE constraint, Paris, November 2023
- Co-organizing the online conference Numerical Analysis, Numerical Modeling, Approximation Theory, Cluj-Napoca, November 2023
- Gave a talk in the workshop Mathematical Modelling, Analysis and Simulation with Applications to Biomedical Processes, Cluj-Napoca, October 2023
- New paper:
*Solving ill-posed Helmholtz problems with physics-informed neural networks*, J. Numer. Anal. Approx. Theory 52 (2023), no. 1, pp. 90-101 - Gave a talk at the 10th Congress of Romanian Mathematicians, Pitești, July 2023
- Co-organized the online conference Numerical Analysis, Numerical Modeling, Approximation Theory, Cluj-Napoca, October 2022
- Gave a talk at the 15th French-Romanian Colloquium on Applied Mathematics, Toulouse, September 2022
- Gave a talk at the 11th European Solid Mechanics Conference, Galway, July 2022
- New paper: E. Burman, M. Nechita, L. Oksanen,
*A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime*, Numer. Math. 150 (2022), pp. 769-801.

**Academic positions:**

- 03/2023 – present: lecturer at Babeș-Bolyai University
- 08/2022 – present: scientific researcher II at Tiberiu Popoviciu Institute of Numerical Analysis
- 03/2022 – 07/2022: scientific researcher at Tiberiu Popoviciu Institute of Numerical Analysis
- 11/2020 – 02/2022: postdoctoral researcher at Inria Paris
- 09/2016 – 09/2020: teaching assistant at University College London
- 05/2016 – 08/2016: scientific researcher at Tiberiu Popoviciu Institute of Numerical Analysis
- 09/2014 – 04/2016: research assistant at Tiberiu Popoviciu Institute of Numerical Analysis

**Education:**

2016-2020 | PhD in Mathematics University College London, UK Thesis: Unique continuation problems and stabilised finite element methods Supervisors: Erik Burman and Lauri Oksanen |

2014-2016 | Master in Applied Mathematics Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca |

2011-2014 | Degree in Mathematics and Computer Science Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca |

**Honours and awards:**

2020 | Sir George Jessel studentship, UCL |

2018 | Andrew Rosen prize for applied mathematics, UCL |

2018 | Sir George Jessel studentship, UCL |

2016 | PhD scholarship, UCL |

2016 | Scientic performance scholarship, Babeș-Bolyai University |

2013 | 3rd Prize, Traian Lalescu National Mathematics Contest for Students, Alba-Iulia |

2011 | Silver Medal and Mention, National Mathematical Olympiad, Final Round, Oradea |

**Conferences and workshops:**

- Simulation of data assimilation under PDE constraint, Paris, talk, 11/2023
- Numerical Analysis, Numerical Modeling, Approximation Theory, Cluj-Napoca, talk, 11/2023
- Mathematical Modelling, Analysis and Simulation with Applications to Biomedical Processes, Cluj-Napoca, talk, 10/2023
- 10th Congress of Romanian Mathematicians, Pitești, talk 07/2023
- Numerical Analysis, Numerical Modeling, Approximation Theory, Cluj-Napoca, talk 10/2022
- 15th French-Romanian Colloquium on Applied Mathematics, Toulouse, talk 09/2022
- 11th European Solid Mechanics Conference, Galway, talk, 07/2022
- Conferința Cercetării Științifice din Academia Română, talk, 11/2021
- Zilele Academice Clujene, talk, 10/2021
- 29th IFIP TC7 Conference on System Modeling and Optimization, talk, 09/2021
- 18th European Finite Element Fair, Inria Paris, 09/2021
- Control in Times of Crisis Seminar, talk, 01/2021
- ICIAM, talk in the Inverse Problems in Shape and Geometry minisymposium, Valencia, 07/2019
- Applied Inverse Problems, Grenoble, talk in the Computational Methods for Inverse Problems minisymposium (co-organised with Lauri Oksanen), 07/2019
- Computational Methods for Interface Problems, UCL, 01/2019
- Inverse and Spectral Problems for (Non)-Local Operators, poster, Leipzig, 09/2018
- Inverse Problems: Modeling and Simulation, poster, Malta, 05/2018
- Inverse Problems Network Meeting 3, awarded the poster prize, UCL, 04/2018
- Inverse Problems Seminar, talk, UCL, 10/2017
- Summer School in Microlocal Analysis and Applications, Cardiff, 06/2017
- Numerical Analysis for PDEs, University of Warwick, 04/2017
- Wave Propagation in Complex Domains, UCL, 03/2017
- Carleman Estimates, Unique Continuation and Applications, UCL, 11/2016
- Zilele Academice Clujene, talk, 05/2016
- Analytical and Computer Assisted Methods in Mathematical Models, Summer School, Debrecen, 09/2013

**Book: **

**Articles:**

- E. Burman, M. Nechita, L. Oksanen,
*Optimal finite element approximation of unique continuation*, arXiv 2311.07440 (2023). - M. Nechita,
*Solving ill-posed Helmholtz problems with physics-informed neural networks*, J. Numer. Anal. Approx. Theory 52 (2023), no. 1, pp. 90-101. - E. Burman, M. Nechita, L. Oksanen,
*A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime*, Numer. Math. 150 (2022), pp. 769-801. - M. Nechita,
*On high-order conforming finite element methods for ill-posed Helmholtz problems*, preprint, 2022. - C.D. Alecsa, I. Boros, F. Frank, P. Knabner, M. Nechita, A. Prechtel, A. Rupp, N. Suciu,
*Numerical benchmark study for flow in highly heterogeneous aquifers*, Adv. Water Res., 138 (2020), 103558. - C.D. Alecsa, I. Boros, F. Frank, P. Knabner, M. Nechita, A. Prechtel, A. Rupp, N. Suciu,
*Benchmark for numerical solutions of flow in heterogeneous groundwater formations*, arxiv 1911.10774. - E. Burman, M. Nechita, L. Oksanen,
*A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime*, Numer. Math. 144 (2020), pp. 451-477. - E. Burman, M. Nechita, L. Oksanen,
*Unique continuation for the Helmholtz equation using stabilized finite element methods*, J. Math. Pures Appl. 129 (2019), pp. 1-22. - G. Moroșanu, M. Nechita,
*Invariant sets and attractors for Hanusse-type chemical systems with diffusions*, Comput. Math. Appl., 73 (2017) 1815–1823.

PhD Thesis:

Currently giving lectures and problem classes on Mathematical Analysis and Numerical Analysis for undergraduate students in Mathematics and Computer Science at Babeș-Bolyai University.