An a posteriori error estimator for a LPS method for Navier–Stokes equations

Araya, Rodolfo; Rebolledo, Ramiro

doi:10.1016/j.apnum.2017.12.018

Cited by 3 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The error analysis of upper and lower bounds avoids the use of saturation assumption. Although the construction of auxiliary space needs a transformation operator in the reference element, it provides a novel idea for removing saturation assumption in reliability analysis [2,3,4,5]. Hakula et al constructed the auxiliary space directly on each element for the second order elliptic problem and elliptic eigenvalue problem and proved that the error is bounded by the error estimator up to oscillation terms without the saturation assumption [17,15].…”

Section: Introductionmentioning

confidence: 99%

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

Zhang,

Wang

2022

Preprint

View full text Add to dashboard Cite

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems corresponding to the degree of freedom of velocity and pressure respectively, which reduces the computational cost sharply. The upper and lower bounds up to an oscillation term of the error estimator are also shown to address the reliability of the adaptive method without saturation assumption. Numerical simulations are performed to demonstrate the effectiveness and robustness of our algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

Zhang,

Wang

2022

Preprint

View full text Add to dashboard Cite

show abstract

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

Zhang

Wang

2022

J Sci Comput

View full text Add to dashboard Cite

A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques

Zhang

2022

Computational Methods in Applied Mathematics

View full text Add to dashboard Cite

Based on a hierarchical basis a posteriori error estimator, an adaptive weak Galerkin finite element method (WGFEM) is proposed for the Stokes problem in two and three dimensions. In this paper, we propose two novel diagonalization techniques for velocity and pressure, respectively. Using diagonalization techniques, we need only to solve two diagonal linear algebraic systems corresponding to the degree of freedom to get the error estimator. The upper bound and lower bound of the error estimator are also shown to address the reliability of the adaptive method. Numerical simulations are provided to demonstrate the effectiveness and robustness of our algorithm.

show abstract

An a posteriori error estimator for a LPS method for Navier–Stokes equations

Cited by 3 publications

References 21 publications

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques

A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques

Contact Info

Product

Resources

About