@Article{cmes.2020.010874,
AUTHOR = {Abdelkarim El Kahoui, Mustapha Malek, Nouh Izem, M. Shadi Mohamed, Mohammed Seaid},
TITLE = {Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using <i>p</i>-Version Refinement},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {124},
YEAR = {2020},
NUMBER = {1},
PAGES = {61--78},
URL = {http://www.techscience.com/CMES/v124n1/39382},
ISSN = {1526-1506},
ABSTRACT = {We propose a high-order enriched partition of unity finite element
method for linear and nonlinear time-dependent diffusion problems. The solution
of this class of problems often exhibits non-smooth features such as steep gradients and boundary layers which can be very challenging to recover using the conventional low-order finite element methods. A class of steady-state exponential
functions has been widely used for enrichment and its performance to numerically
solve these challenges has been demonstrated. However, these enrichment functions have been used only in context of the standard <i>h</i>-version refinement or
the so-called <i>q</i>-version refinement. In this paper we demonstrate that the <i>p</i>-version
refinement can also be a very attractive option in terms of the efficiency and the
accuracy in the enriched partition of unity finite element method. First, the transient diffusion problem is integrated in time using a semi-implicit scheme and the
semi-discrete problem is then integrated in space using the <i>p</i>-version enriched
finite elements. Numerical results are presented for three test examples of timedependent diffusion problems in both homogeneous and heterogeneous media.
The computed results show the significant improvement when using the <i>p</i>-version
refined enriched approximations in the finite element analysis. In addition, these
results support our expectations for a robust and high-order accurate enriched partition of unity finite element method.},
DOI = {10.32604/cmes.2020.010874}
}