2025/06/04 by Ankit Kumar, Kumar, Ankit, Sarvesh Kumar +3
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2506.03751
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.