On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

2021 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Edge Based

scholarly journals A Note on Multilevel Based Error Estimation

2016 ◽  
Vol 16 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Helmut Harbrecht ◽  
Reinhold Schneider
Keyword(s):  
Finite Element ◽  
Poisson Equation ◽  
Error Estimation ◽  
Finite Element Approximation ◽  
Error Estimator ◽  
Element Approximation ◽  
Finite Element Approximations ◽  
The Poisson Equation ◽  
Galerkin Solution ◽  
Edge Based

AbstractBy employing the infinite multilevel representation of the residual, we derive computable bounds to estimate the distance of finite element approximations to the solution of the Poisson equation. If the finite element approximation is a Galerkin solution, the derived error estimator coincides with the standard element and edge based estimator. If Galerkin orthogonality is not satisfied, then the discrete residual additionally appears in terms of the BPX preconditioner. As a by-product of the present analysis, conditions are derived such that the hierarchical error estimation is reliable and efficient.

scholarly journals Higher-order finite element approximation of the dynamic Laplacian

2020 ◽  
Vol 54 (5) ◽  
pp. 1777-1795
Author(s):  
Nathanael Schilling ◽  
Gary Froyland ◽  
Oliver Junge
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Element ◽  
Laplace Operator ◽  
Finite Time ◽  
Fluid Flows ◽  
Finite Element Approximation ◽  
Higher Order ◽  
Element Approximation ◽  
Eigenvalues And Eigenvectors ◽  
Order Element

The dynamic Laplace operator arises from extending problems of isoperimetry from fixed manifolds to manifolds evolved by general nonlinear dynamics. Eigenfunctions of this operator are used to identify and track finite-time coherent sets, which physically manifest in fluid flows as jets, vortices, and more complicated structures. Two robust and efficient finite-element discretisation schemes for numerically computing the dynamic Laplacian were proposed in Froyland and Junge [SIAM J. Appl. Dyn. Syst. 17 (2018) 1891–1924]. In this work we consider higher-order versions of these two numerical schemes and analyse them experimentally. We also prove the numerically computed eigenvalues and eigenvectors converge to the true objects for both schemes under certain assumptions. We provide an efficient implementation of the higher-order element schemes in an accompanying Julia package.

scholarly journals Two-Level Finite Element Approximation for Oseen Viscoelastic Fluid Flow

Mathematics ◽  
2018 ◽  
Vol 6 (5) ◽  
pp. 71 ◽  
Author(s):  
Nasrin Nasu ◽  
Md. Mahbub ◽  
Shahid Hussain ◽  
Haibiao Zheng
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Viscoelastic Fluid ◽  
Finite Element Approximation ◽  
Element Approximation
Sign in / Sign up

Export Citation Format

Share Document