By utilizing a symmetric dual-wind DG (DWDG) spatial discretization and a backward Euler temporal discretization, we proposed a fully discrete scheme designed to solve a parabolic variational inequality. We also determined the rate of convergence of the error in space and time in suitable norms.
We proposed and analyzed a numerically stable and convergent scheme for the convection-diffusion (CD) equation in the convection-dominated regime and derived a local order of convergence of $O(ℎ^{1.5})$ whenever the exact solution is of $𝐻^2(\Omega)$ regularity. The following figures illustrate a comparison between the exact and numerical solution from a particular numerical experiment.
We proposed a numerical scheme to reduce an elliptic optimal control problem with control constraints to a finite-dimensional optimization problem with equality and inequality-type constraints and established the order of convergence of the error as we refine the triangulation of the polygonal domain $\Omega \subset \mathbb{R}^2$. The figures below present a comparison between the exact solutions and numerical solutions from a specific numerical experiment.
Bommana Boyana, S., Lewis, T., Liu, S., Zhang, Y. (2025). Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints. Results in Applied Mathematics, Volume 27, 2025, 100624, ISSN 2590-0374.
https://doi.org/10.1016/j.rinam.2025.100624
Supported by NSF grants DMS-2111004 (PI: Y. Zhang), DMS-2111059 (PI: T. Lewis), and Florida Polytechnic University research start-up grant (Satyajith Bommana Boyana)
Boyana, S.B., Lewis, T., Liu, S., Zhang, Y. (2024). Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem. Journal of Computers and Mathematics with Applications, Volume 175, 2024, Pages 224-235, ISSN 0898-122.
https://doi.org/10.1016/j.camwa.2024.09.027
Supported by NSF grants DMS-2111004 (PI: Y. Zhang), DMS-1929284 (PI: S. Liu), and DMS-2111059 (PI: T. Lewis)
Bommana Boyana, S., Lewis, T., Rapp, A., Zhang, Y. (2023). Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic variational inequality. Journal of Computational and Applied Mathematics, 422, 114922.
https://doi.org/10.1016/j.cam.2022.114922
Supported by NSF grants DMS-2111004 (PI: Y. Zhang), and DMS-2111059 (PI: T. Lewis)
Bommana Boyana, S., Lewis, T., Liu, S., Zhang, Y. Convergence Analysis of Discontinuous Galerkin Methods for an Optimal Control Problem with a Convection-Dominated State Equation.
Asaithambi A., Asaithambi G., Bommana Boyana, S., Zhang, Y. Computational Analysis of Thrombolysis in Acute Ischemic Stroke: Exploring a Novel Therapeutic Approach.
