8 citations · 14 across the 9 of their papers we have counts for
10 papers
High-order mass-, energy- and momentum-conserving methods for the nonlinear Schrödinger equation
Georgios Akrivis, Buyang Li, Rong Tang +1
This paper introduces a novel formulation and an associated space-time finite element method for simulating solutions to the nonlinear Schrödinger equation. A major advantage of th…
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…
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…
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…
The weighted and shifted seven-step BDF method for parabolic equations
Georgios Akrivis, Minghua Chen, Fan Yu
Stability of the BDF methods of order up to five for parabolic equations can be established by the energy technique via Nevanlinna--Odeh multipliers. The nonexistence of Nevanlinna…
The energy technique for the six-step BDF method
Georgios Akrivis, Minghua Chen, Fan Yu +1
In combination with the Grenander--Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental requirement of the Nevanlinna--O…
Higher-order linearly implicit full discretization of the Landau--Lifshitz--Gilbert equation
Georgios Akrivis, Michael Feischl, Balázs Kovács +1
For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order combined with h…
Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
Georgios Akrivis, Buyang Li, Christian Lubich
We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay…
Maximum norm analysis of implicit-explicit backward difference formulas for nonlinear parabolic equations
Georgios Akrivis, Buyang Li
We establish optimal order a priori error estimates for implicit-explicit BDF methods for abstract semilinear parabolic equations with time-dependent operators in a complex Banach…