13th International Workshop on Variational Multiscale and Stabilized Finite Elemements (VMS 18) - Abstract
Jha, Abhinav
Algebraic stabilizations, also called Algebraic Flux Correction (AFC) schemes, belong to the very few finite element discretizations of steady-state convection-diffusion equations that obey the discrete maximum principle. However, appropriate limiters depend on the solution itself, thus leading to a nonlinear discrete problem. The efficient solution of these nonlinear problems seems currently to be the biggest drawback in the application of these schemes.
In this talk, several methods for solving the nonlinear problems are discussed. The focus is particularly on fixed point iterations and Newton's method, thereby discussing regularizations of the limiters to obtain differentiable expressions. The methods are compared on parameters such as number of iterations and the time taken to solve the problem. Two limiters will be considered, the traditional Kuzmin limiter and a recently proposed limiter that is linearity preserving, i.e. the BJK limiter. Different algorithmic components such as Anderson acceleration, dynamic damping and projection to admissible values will also be discussed. Numerical examples from 2d as well as 3d assess the different iterative schemes.