4 papers
Implicit and implicit--explicit high-order BDF methods for coupled elliptic--parabolic systems
Georgios Akrivis, Minghua Chen, Fan Yu
First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., M…
Runge-Kutta Physics Informed Neural Networks: Formulation and Analysis
Georgios Akrivis, Charalambos G. Makridakis, Costas Smaragdakis
In this paper we consider time-dependent PDEs discretized by a special class of Physics Informed Neural Networks whose design is based on the framework of Runge--Kutta and related…
A priori and a posteriori error estimates for discontinuous Galerkin time-discrete methods via maximal regularity
Georgios Akrivis, Stig Larsson
The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori…
Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity
Georgios Akrivis, Stig Larsson
We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posterior…