Aposteriori error estimation of Subgrid multiscale stabilized finite element method for transient Stokes model

TL;DR

This paper introduces a new stabilized finite element method using subgrid multiscale techniques for the transient Stokes model, providing stability analysis, error estimates, and numerical verification of convergence.

Contribution

It develops an a posteriori error estimation framework for the stabilized subgrid multiscale finite element method applied to the transient Stokes problem, including stability and convergence analysis.

Findings

Proven discrete inf-sup condition for pressure stabilization

Derived a posteriori error estimates for the scheme

Numerical experiments confirm theoretical convergence order

Abstract

In this study, we present a novel stabilized finite element analysis for transient Stokes model. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the stabilized form as well as stability analysis of it's fully discrete formulation are presented elaborately. Discrete $inf$-$sup$ condition for pressure stabilization has been proven. For the time discretization the fully implicit schemes have been used. A detailed derivation of the aposteriori error estimate for the stabilized subgrid multiscale finite element scheme has been presented. Numerical experiment has been carried out to verify theoretically established order of convergence.