Research interests
My research sits at the intersection of computational mathematics, numerical analysis, and scientific computing, with a particular emphasis on stabilized finite element methods for convection-dominated and multiscale partial differential equations arising in fluid dynamics, heat and mass transfer, and transport phenomena.
A central theme of my work is the application, development, and analysis of stabilized finite element frameworks — such as Streamline-Upwind/Petrov-Galerkin (SUPG), Variational Multiscale (VMS), and the YZβ shock-capturing — for nonlinear, high-Reynolds-number, and thermochemical nonequilibrium systems. More recently, I have been actively pursuing hybrid numerical–machine learning methodologies, integrating physics-informed neural networks (PINNs) with stabilized finite element solvers to enhance robustness, accuracy, and computational efficiency in regimes where classical methods alone face limitations.
Topics I work on
– Stabilized finite element methods (SUPG, VMS, YZβ shock-capturing)
– Convection-dominated PDEs and boundary/interior layer problems
– Computational fluid dynamics (CFD) — high-speed, hypersonic, thermochemical nonequilibrium, and MHD flows
– Heat and mass transfer, natural/mixed convection, nanofluids
– Hybrid PINN–FEM frameworks and scientific machine learning
– Asymptotic methods for singularly perturbed problems
Current research directions
– Hybrid PINN–FEM frameworks — coupling physics-informed neural networks with stabilized finite element solvers for forward and inverse problems in convection-dominated regimes.
Ongoing TÜBİTAK CAREER project. – Stabilized FEM for haptotaxis-driven cancer invasion — SUPG-based discontinuity-capturing formulations for tumor-invasion models.
Ongoing TÜBİTAK 1002 project.
– Dendrite formation control in lithium-metal batteries — combining numerical simulation with experimental validation and fast-charging optimization (joint work with B. Emek Abalı, Uppsala University, starting November 2026). TÜBİTAK 2219 fellowship.
– High-speed flows with YZβ shock-capturing — hypersonic and thermochemical nonequilibrium simulations, in collaboration with Ö. Uğur (METU).
Funded research projects
I have served as Principal Investigator on multiple research projects funded by TÜBİTAK (The Scientific and Technological Research Council of Turkey).
– TÜBİTAK 2219 (2026–2027) — Dendrite Formation Control in Lithium-Metal Batteries: Numerical Simulation, Experimental Validation, and Fast-Charging Optimization. International Postdoctoral Research Fellowship.
– TÜBİTAK 3501 CAREER (2026, Project ID: 225M468) — Development of a Stabilized Finite Element Framework Enhanced with Physics-Informed Neural Networks for Computing Convection-Dominated Flows.
– TÜBİTAK 1002 (2025, Project ID: 125F320) — Stabilized Finite Element Simulations of Haptotactic Tumor Invasion in Convection-Dominated Environments.
– TÜBİTAK 2219 (2023–2024) — Stabilized finite element methods for simulating convection-dominated multicomponent transport phenomena.
Selected publications
For the complete list, please visit my Google Scholar and ResearchGate profiles. Representative recent works:
– Cengizci S., Uğur Ö., Natesan S. A PINN-enhanced SUPG-stabilized hybrid finite element framework with shock-capturing for computing steady convection-dominated flows. Advances in Engineering Software, 2026.
– Cengizci S., Öztop H. F., Natesan S. A discontinuity-capturing SUPG finite element framework for simulating haptotaxis-driven cancer invasion. Mathematics and Computers in Simulation, 241:271–292, 2026.
– Cengizci S., Uğur Ö. A computational study for pricing European- and American-type options under Heston’s stochastic volatility model: application of the SUPG-YZβ formulation. Computational Economics, 66:179–206, 2025.
– Cengizci S., Uğur Ö. A computational study for simulating MHD duct flows at high Hartmann numbers using a stabilized finite element formulation with shock-capturing. Journal of Computational Science, 81:102381, 2024.
– Cengizci S., Uğur Ö., Natesan S. SUPG-based stabilized finite element computations of convection-dominated 3D elliptic PDEs using shock-capturing. Journal of Computational and Applied Mathematics, 451:116022, 2024.
Preprints and ongoing work
– Cengizci S. Three-dimensional simulations of convection-dominated PDEs via a hybrid stabilized FEM–PINN coupling: the PASSC framework. Submitted to Computational Mechanics, 2026.
– Cengizci S., Uğur Ö., Natesan S. Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems. Submitted to Computer Physics Communications, 2026.
Recent Talks
- Sep 2026 — ICAME’26, Cunda, Turkey. PINNs meet stabilized finite element methods for time-dependent convection-dominated PDEs.
- Jul 2026 — 15th AIMS Conference, Athens, Greece. Hybrid PINN-FEM framework for tumor growth models with stabilisation.
- Jul 2026 — 15th AIMS Conference, Athens, Greece. Bridging machine learning and stabilized FEM: a hybrid PINN-SUPG framework for 3D transport equations.
- Jun 2026 — International Conference of Young Mathematicians (online), Kyiv, Ukraine. Enhancing Shock Resolution in the Sod Shock Tube Problem via the PASSC Framework.
Selected Talks
- Oct 2025 — UNCG Virtual PDE Conference, Greensboro, USA. A hybrid machine learning framework for solving convection-dominated steady-state transport problems.
- Jun 2024 — ICAME’24, Balıkesir, Turkey. An application of the SUPG/PSPG finite element formulation for simulating natural convection heat transfer inside nanoliquid-filled 2D cavities.
- May 2024 — CMES-2024, Şanlıurfa, Turkey. Applications of the SUPG-YZβ finite element formulation: from mussel-algae interactions to Schnakenberg reaction models.
- Apr 2024 — ICMMAAC-24, Beirut, Lebanon. Finite element analysis of natural convection phenomena occurring within nanofluid-filled 3D cavities.
For a complete list of conference presentations, see my CV.
Research group
I lead the SCaDA Lab (Scientific Computing and Data Analysis Lab) at Antalya Bilim University. Students working with me focus on stabilized finite element methods, computational fluid dynamics, and hybrid numerical–machine learning techniques. Project documentation, weekly notes, and contribution guidelines are maintained in our lab wiki.
Academic service
I regularly serve as a reviewer for international journals indexed in Web of Science, including Journal of Computational Physics, Computational Mechanics, International Journal for Numerical Methods in Engineering, Physics of Fluids, Computers and Mathematics with Applications, Mathematics and Computers in Simulation, Numerical Heat Transfer, and ZAMM, among others.
Academic awards
– Doctoral Thesis Award, Middle East Technical University (2023)
– Academic Performance Award, Antalya Bilim University (2022)
– Academic Publication Encouragement Award, Antalya Bilim University (×3)
– TÜBİTAK UBYT Publication Encouragement Award (×9)
Collaborations
I am always open to discussions and potential collaborations in the areas of stabilized finite element methods, computational fluid dynamics, and physics-informed machine learning. Feel free to get in touch by e-mail.