A STUDY ON DISCONTINUOUS GALERKIN SCHEME FOR SOLVING AGGREGATION-BREAKAGE EQUATIONS

Abstract

This project is dedicated to the study of higher order Discontinuous Galerkin(DG) method and trying to applying on coagulation-fragmentation equations . In this project, we embark on a detailed exploration of the high order discontinuous Galerkin (DG) method, starting with an overview of its fundamental principles. Following this, we delve into the specifics of the model problem concerning coagulation-fragmentation equations, providing a comprehensive understanding of the system under investigation. Our approach involves breaking down the equations into smaller parts, analyzing them. We apply the DG method to a version of the equations that maintains conservation properties, which is important for accurately simulating physical systems. To discretize the equations, we use a technique called Gaussian quadrature, where we evaluate the flux terms using a specific number of quadrature points determined by the polynomial degree. This helps us accurately capture the behavior of the system. Throughout our investigation, we emphasize the importance of proper time discretization and adherence to specific time step restrictions to uphold the positivity of cell averages over time. By the conclusion of this project, we aim to offer a robust computational analysis framework for tackling coagulation-fragmentation equations, shedding light on the intricate behaviours exhibited by such systems.