Explicit T-coercivity for the Stokes problem: A coercive finite element discretization

Patrick Ciarlet; Erell Jamelot

doi:10.1016/j.camwa.2025.03.028

Explicit T-coercivity for the Stokes problem: A coercive finite element discretization

Patrick Ciarlet
, Erell Jamelot

Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Using the T-coercivity theory as advocated in Chesnel and Ciarlet (2013) [25], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small.

Original language	English
Pages (from-to)	137-159
Number of pages	23
Journal	Computers and Mathematics with Applications
Volume	188
DOIs	https://doi.org/10.1016/j.camwa.2025.03.028
Publication status	Published - 15 Jun 2025

Keywords

Stabilized P × P pair
Stokes problem
T-coercivity

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10.1016/j.camwa.2025.03.028

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abstract = "Using the T-coercivity theory as advocated in Chesnel and Ciarlet (2013) [25], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small.",

keywords = "Stabilized P {\texttimes} P pair, Stokes problem, T-coercivity",

author = "Patrick Ciarlet and Erell Jamelot",

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T2 - A coercive finite element discretization

AU - Ciarlet, Patrick

AU - Jamelot, Erell

PY - 2025/6/15

Y1 - 2025/6/15

N2 - Using the T-coercivity theory as advocated in Chesnel and Ciarlet (2013) [25], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small.

AB - Using the T-coercivity theory as advocated in Chesnel and Ciarlet (2013) [25], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small.

KW - Stabilized P × P pair

KW - Stokes problem

KW - T-coercivity

UR - https://www.scopus.com/pages/publications/105001677969

U2 - 10.1016/j.camwa.2025.03.028

DO - 10.1016/j.camwa.2025.03.028

M3 - Article

AN - SCOPUS:105001677969

SN - 0898-1221

VL - 188

SP - 137

EP - 159

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

Explicit T-coercivity for the Stokes problem: A coercive finite element discretization

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Keywords

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