TY - JOUR
T1 - A New Multiphysics Finite Element Method for a Biot Model with Secondary Consolidation
AU - Ge , Zhihao
AU - He , Wenlong
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 515
EP - 550
PY - 2024
DA - 2024/08
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2023-0011
UR - https://global-sci.org/intro/article_detail/csiam-am/23307.html
KW - Biot model, multiphysics finite element method, optimal convergence order, secondary consolidation.
AB - <p style="text-align: justify;">In this paper, we propose a new multiphysics finite element method for
a Biot model with secondary consolidation in soil dynamics. To better describe the
multiphysical processes underlying in the original model and propose stable numerical methods to overcome “locking phenomenon” of pressure and displacement, we
reformulate the swelling clay model with secondary consolidation by a new multiphysics approach, which transforms the fluid-solid coupling problem to a fluid coupled problem. Then, we give the energy law and prior error estimate of the weak
solution. Also, we design a fully discrete time-stepping scheme to use multiphysics
finite element method with $P_2−P_1−P_1$ element pairs for the space variables and backward Euler method for the time variable, and we derive the discrete energy laws and
the optimal convergence order error estimates. Also, we show some numerical examples to verify the theoretical results and there is no “locking phenomenon”. Finally, we
draw conclusions to summarize the main results of this paper.</p>