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math.NA2026
A Weighted Upwind Vector Kinetic Lattice Boltzmann Method For Hyperbolic Conservation Laws
Michael W. Brown, Jehanzeb Chaudhry, John N. Shadid
Vector kinetic lattice Boltzmann (VKLB) methods have recently emerged as a promising framework for solving hyperbolic partial differential equation (PDE) systems. VKLB discretizes…
math.NA2025
Adjoint-based A Posteriori Error Analysis for Semi-explicit Index-1 and Hessenberg Index-2 Differential-Algebraic Equations
Jehanzeb H. Chaudhry, Owen L. Lewis, Md Al Amin Molla
In this work we develop adjoint-based analyses for \textit{a posteriori} error estimation for the temporal discretization of differential-algebraic equations (DAEs) of special type…