Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error Estimates of a Fully Discrete Multiphysics Finite Element Method
  for a Nonlinear Poroelasticity Model   In this paper, we propose a multiphysics finite element method for a
nonlinear poroelasticity model. To better describe the processes of deformation
and diffusion, we firstly reformulate the nonlinear fluid-solid coupling
problem into a fluid-fluid coupling problem by a multiphysics approach. Then 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 adopt the Newton iterative method to
deal with the nonlinear term. Also, we derive the discrete energy laws and the
optimal convergence order error estimates without any assumption on the
nonlinear stress-strain relation. Finally, we show some numerical examples to
verify the rationality of theoretical analysis and there is no "locking
phenomenon".

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th