Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection
Numerical Analysis
2025-06-05 v1 Numerical Analysis
Abstract
We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and L2-norm. Several numerical experiments are conducted to validate the theoretical findings and assess the computational efficiency of the proposed numerical methods.
Cite
@article{arxiv.2506.03751,
title = {Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection},
author = {Ankit Kumar and Sarvesh Kumar and Sangita Yadav},
journal= {arXiv preprint arXiv:2506.03751},
year = {2025}
}