A new modified Galerkin method for the two-dimensional Navier-Stokes equations

TL;DR

This paper introduces a novel multi-level modified Galerkin method for the 2D Navier-Stokes equations, improving approximation accuracy by iteratively refining solutions based on induced trajectories.

Contribution

It develops a new multi-level Galerkin approach that enhances solution accuracy for the 2D Navier-Stokes equations using induced trajectories.

Findings

Provides a construction with multiple levels for better accuracy.

Uses induced trajectories to define approximate solutions.

Offers a framework for iterative solution refinement.

Abstract

We present a new type of modified Galerkin method. It is a construction with several (inductively defined) levels, that provides approximate solutions of increasing accuracy with every new level. These solutions are constructed as approximations of the so called induced trajectories (notion on which the definition of a class of approximate inertial manifolds used in the nonlinear and postprocessed Galerkin methods is based).