Paper Info
Title
A partition of unity finite element method for nonlinear transient diffusion problems in heterogeneous materials
Abstract
This work studies for the first time the solution of a nonlinear problem using an enriched finite element approach. Such problems can be highly demanding computationally. Hence, they can significantly benefit from the efficiency of the enriched finite elements. A robust partition of unity finite element method for solving transient nonlinear diffusion problems is presented. The governing equations include nonlinear diffusion coefficients and/or nonlinear source terms in both homogeneous and heterogeneous materials. To integrate the equations in time, we consider a linearly semi-implicit scheme in the finite element framework. As enrichment procedures, we consider a combination of exponential expansions to be injected in the finite element basis functions on coarse meshes. The proposed method shows a large reduction in the number of degrees of freedom required to achieve a fixed accuracy compared to the conventional finite element method. In addition, the proposed partition of unity method shows a stable behavior in treating both internal and external boundary layers in nonlinear diffusion applications. The performance of the proposed method is also used for the numerical simulation of heat conduction in functionally graded materials.
Year
DOI
Venue
2019
10.1007/s40314-019-0782-z
COMPUTATIONAL & APPLIED MATHEMATICS
Keywords
DocType
Volume
Nonlinear problems,Diffusion equation,Partition of unity method,Finite element method,Heat transfer,Heterogeneous material,Functionally graded material
Journal
38
Issue
ISSN
Citations 
2.0
2238-3603
0
PageRank 
References 
Authors
0.34
4
5
Name
Order
Citations
PageRank
Mustapha Malek101.01
Nouh Izem200.68
Mohammed Seaïd35416.35
M. Shadi Mohamed463.21
Mohamed Wakrim523.47