Recent advances in technology and refinement of available computational resources paved
the way for the extensive use of computers to model and simulate complex real-world …

This paper presents a comprehensive review of finite element methods (FEMs) applied to a
diverse range of reaction-diffusion equations (RDEs). Beginning with a historical overview of …

The integration of graph neural networks (GNNs) and neural ordinary and partial differential
equations has been extensively studied in recent years. GNN architectures powered by …

Deep learning methods have gained considerable interest in the numerical solution of
various partial differential equations (PDEs). One particular focus is physics-informed neural …

In this paper, we develop a compact direct radial basis function partition of unity (D-RBF-PU)
method for parabolic equations on closed surfaces. The new method involves partitioning …

We discretise a tangential tensor field equation using a surface-finite element approach with
a penalisation term to ensure almost tangentiality. It is natural to measure the quality of such …

The crystallization is a typical process in material science and this process can be described
by the phase-field crystal type models. To investigate the dynamics of phase-field crystal …

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element
Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial …

Herein, we propose a practical numerical method for solving two-component phase-field
crystal model with vacancy effect on curved surfaces and perform various numerical …

We study the implementation of a Chebyshev spectral method with forward Euler integrator
proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of …