scholarly journals Equivalent Finite Element Formulations for the Calculation of Eigenvalues Using Higher-Order Polynomials

2012 ◽  
Vol 1 (1) ◽  
pp. 13-23 ◽  
Author(s):  
C. G. Provatidis
Keyword(s):  
Finite Element ◽  
Higher Order ◽  
Finite Element Formulations

Efficient Higher Order Nodal Finite Element Formulations for Neutron Multigroup Diffusion Equations

1996 ◽  
Vol 124 (1) ◽  
pp. 97-110 ◽  
Author(s):  
J. P. Hennart ◽  
E. M. Malambu ◽  
E. H. Mund ◽  
E. del Valle
Keyword(s):  
Finite Element ◽  
Higher Order ◽  
Diffusion Equations ◽  
Finite Element Formulations

Higher-order finite element for sandwich plates

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 525-533
Author(s):  
S. Oskooei ◽  
J. S. Hansen
Keyword(s):  
Finite Element ◽  
Higher Order ◽  
Sandwich Plates

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

Error analysis of higher order trace finite element methods for the surface Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Jankuhn ◽  
Maxim A. Olshanskii ◽  
Arnold Reusken ◽  
Alexander Zhiliakov
Keyword(s):  
Finite Element ◽  
Stokes System ◽  
Parametric Representation ◽  
Higher Order ◽  
Optimal Order ◽  
Helmholtz Instability ◽  
Surface Stability ◽  
Instability Problem ◽  
Convergence Results ◽  
Optimal Order Convergence

AbstractThe paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.

Implicit time discretization schemes for mixed least-squares finite element formulations

2020 ◽  
Vol 368 ◽  
pp. 113111
Author(s):  
Solveigh Averweg ◽  
Alexander Schwarz ◽  
Carina Nisters ◽  
Jörg Schröder
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Time Discretization ◽  
Implicit Time ◽  
Discretization Schemes ◽  
Finite Element Formulations
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