Journal ArticleDOI
An adaptive finite element method for a time‐dependent Stokes problem
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TLDR
An a posteriori error analysis of the two‐dimensional time‐dependent Stokes problem with homogeneous Dirichlet boundary conditions is conducted, which can be extended to mixed boundary conditions and an adaptive space/time mesh refinement strategy is developed.About:
This article is published in Numerical Methods for Partial Differential Equations.The article was published on 2019-01-01. It has received 5 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Finite element method.read more
Citations
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Journal ArticleDOI
An MHD Stokes eigenvalue problem and its approximation by a spectral collocation method
Önder Türk,Önder Türk +1 more
TL;DR: The effects of introducing a magnetic field on the eigenspectrum focusing mainly on the change of the fundamental eigenpairs, and the consequential variation of the eigenstructure with the magnetic field are presented.
Journal ArticleDOI
A New Nodal Stress Recovery Technique in Finite Element Method Using Colliding Bodies Optimization Algorithm
Ali Kaveh,M. R. Seddighian +1 more
TL;DR: A new nodal stress recovery technique is proposed in which Colliding Bodies Optimization Algorithm fits an appropriative function for nodal Stress fields, providing benefits of both analytical approaches and numerical methods.
Journal ArticleDOI
PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers
TL;DR: This paper proposes a new kind of data-driven PDEs solver, physics-informed cell representations (PIXEL), elegantly combining classical numerical methods and learning-based approaches to improve accuracy and convergence and overcome the spectral bias presented in PINNs.
Journal ArticleDOI
Approximation of the Stokes eigenvalue problem on triangular domains using a stabilized finite element method
Önder Türk,Önder Türk +1 more
TL;DR: In this article, a stabilized finite element method for the approximation of the Stokes eigenvalue problem on triangular domains is proposed, which is based on orthogonal scalar scaling.
References
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On the Navier-Stokes equations
TL;DR: In this paper, a criterion for the convergence of numerical solutions of Navier-Stokes equations in two dimensions under steady conditions is given, which applies to all cases, of steady viscous flow in 2D.
Journal ArticleDOI
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
M. Crouzeix,P.-A. Raviart +1 more
TL;DR: Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suited for the numerical treatment of the incompressibility condition are given.
Journal ArticleDOI
Approximation by finite element functions using local regularization
TL;DR: In this paper, the authors give an elementary proof of a theorem of approximation of Sobolev spaces by fimte éléments without to use classical interpolation, which allows us in some cases to fit boundary conditions.
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Francisco Durango,Julia Novo +1 more