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. Read more
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 $\Omega \subset \mathbb{R}^2$. Read more
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. Read more
Boyana, S. B., 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-2111059 (PI: T. Lewis) and DMS-2111004 (PI: Y. Zhang)
Boyana, S. B., Lewis, T., Liu, S., Zhang, Y. Convergence Analysis of a Novel Discontinuous Galerkin Methods for a Convection Dominated Problem. Journal of Computers and Mathematics with Applications.
Manuscript #: CAMWA-D-24-00505
Supported by NSF grants DMS-2111004 (PI: Y. Zhang), DMS-2111059 (PI: T. Lewis) & DMS-1929284 (PI: S. Liu)
Boyana, S. B., Lewis, T., Zhang, Y. Convergence Analysis of a Symmetric Dual-Wind Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with Control Constraints.
Supported by NSF grant DMS-2111004 (PI: Y. Zhang)
