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math.NA2025
An Error Analysis of Second Order Elliptic Optimal Control Problem via Hybrid Higher Order Methods
Gouranga Mallik, Ramesh Chandra Sau
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three…
math.NA2024
A Review of Neural Network Solvers for Second-order Boundary Value Problems
Ramesh Chandra Sau, Luowei Yin
Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high…
math.NA2024
A two-grid Adaptive Finite Element Method for the Dirichlet Boundary Control Problem Governed by Stokes Equation
Thirupathi Gudi, Ramesh Chandra Sau
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to…