Research

My research interests include:

• numerical analysis
• numerical solution of partial differential equations with finite element method
• a posteriori error estimation and adaptivity

Publications

• (2022, with P. Chatzipantelidis) Error analysis of a backward Euler positive preserving stabilized scheme for a Chemotaxis system. [Arxiv]
• (2024) Error analysis of an Algebraic Flux Correction Scheme for a nonlinear Scalar Conservation Law Using SSP-RK2. [Arxiv]
• (2024) A numerical study for the second order modified Patankar-Runge-Kutta method applied to a Chemotaxis system, submitted.
• (2024) Error analysis of a positivity preserving numerical scheme for a viscous Hamilton-Jacobi equation, submitted.

Lecture Material

Here you may find lecture notes from classes that I have taught. (Under construction)

• Notes of numerical methods of ODEs
• Notes of numerical methods of PDEs

Here you may find some collection of programming exercises and their solution that used during my lectures.

• Approximating Ordinary Differential Equations. Some solved exercises.

• Explicit Euler: pdf and here its implemetantion in Python.

• Implicit Euler with Newton method: pdf and here its implemetantion in Python.

• Explicit Euler (System): pdf and here its implemetantion in Python.

• Implicit Euler with Newton method (System): pdf and here its implemetantion in Python.

• Lotka-Volterra Equations: pdf and here its implemetantion in Python with Explicit Euler and Implicit Midpoint Method.

• Explicit Multistep Methods (Adams-Bashforth): pdf and the implemetantion in Python of the corresponding cases for a scalar ODE Case 1, Case 2, Case 3 the implemetantion in Python of the corresponding cases for a system ODE Case 1, Case 2, Case 3.



• Approximating Partial Differential Equations with Finite Element Method (Soon)

CV

• PhD (2023) in Applied and Computational Mathematics Department of Mathematics & Applied Mathematics, University of Crete
• PhD Thesis: Numerical methods for evolutionary differential equations that maintain the positivity of the solution
• Advisor: Panagiotis Chatzipantelidis

• MSc (2017) in Applied Mathematics Department of Mathematics & Applied Mathematics, University of Crete
• Master Thesis: A posteriori error estimation for elliptic equations (in greek)  (Poster)(in greek)
• Advisor: Panagiotis Chatzipantelidis


• BSc (2015) in Mathematics Department of Mathematics & Applied Mathematics, University of Crete