On the error analysis of stabilized finite element methods for the Stokes problem

TL;DR

This paper provides a comprehensive error analysis, both a priori and a posteriori, for stabilized mixed finite element methods applied to the Stokes equations, enhancing understanding of their accuracy and reliability.

Contribution

It offers the first complete error analysis framework for a broad class of stabilized finite element methods for the Stokes problem.

Findings

Establishes error bounds for stabilized methods

Provides guidelines for method selection based on error estimates

Enhances the theoretical understanding of stabilized finite element approaches

Abstract

For a family of stabilized mixed finite element methods for the Stokes equations a complete a priori and a posteriori error analysis is given.