6 papers
Virtual element methods for a quad-curl problem on general planar domains
Susanne C. Brenner, Li-yeng Sung, Jai Tushar
We design and analyze virtual element methods for a quad-curl problem on general polygonal domains that are based on the Hodge decomposition of divergence-free vector fields. Numer…
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Jai Tushar, Arbaz Khan, Manil T. Mohan
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regula…
A natural language framework for non-conforming hybrid polytopal methods in Gridap.jl
Jordi Manyer, Jai Tushar, Santiago Badia
Hybrid finite element methods such as hybridizable discontinuous Galerkin, hybrid high-order and weak Galerkin have emerged as powerful techniques for solving partial differential…
Analysis of BDDC preconditioners for non-conforming polytopal hybrid discretisation methods
Santiago Badia, Jerome Droniou, Jordi Manyer +1
In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; \href{https://doi.org/10.1007…
Optimal Control of Stationary Doubly Diffusive Flows on Lipschitz Domains
Jai Tushar, Arbaz Khan, Manil T. Mohan
In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis ba…
A discrete trace theory for non-conforming polytopal hybrid discretisation methods
Santiago Badia, Jerome Droniou, Jai Tushar
In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defi…