Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges

J Tushar, A Kumar, S Kumar - Computers & Mathematics with Applications, 2022 - Elsevier
In this article, we discuss and analyze a conforming virtual element discretization with
boundary stabilization term proposed in Brenner and Sung (2018)[30](suitable for small …

Mixed virtual element methods for optimal control of Darcy flow

J Tushar, A Kumar, S Kumar - Computers & Mathematics with Applications, 2023 - Elsevier
In this work, we discuss and rigorously analyze a virtual element method for the numerical
approximation of control constrained optimal control problem governed by Darcy flow. In the …

Convergence analysis of virtual element method for the electric interface model on polygonal meshes with small edges

N Kumar, J Tushar, JY Yuan - Computers & Mathematics with Applications, 2024 - Elsevier
A conforming virtual element method is studied for approximating the solution of a pulsed
electric interface model on polygonal meshes with small edges or faces, which traditional …

Mixed virtual element methods for elliptic optimal control problems with boundary observations in L2 (Γ)

M Yang, Z Zhou - Applied Numerical Mathematics, 2024 - Elsevier
In this paper, we study the mixed virtual element approximation to an elliptic optimal control
problem with boundary observations. The objective functional of this type of optimal control …

Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem

J Tushar, RC Sau, A Kumar - Journal of Scientific Computing, 2024 - Springer
This article develops a conforming virtual element method for a control-constrained Dirichlet
boundary optimal control problem governed by the diffusion problem. An energy-based cost …

Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity

H Singh, A Khan - arXiv preprint arXiv:2403.15783, 2024 - arxiv.org
This study introduces the divergence-conforming discontinuous Galerkin finite element
method (DGFEM) for numerically approximating optimal control problems with distributed …