Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems

Fan Chen; Ming Cui; Chenguang Zhou

Applications of Mathematics (2025)

  • Issue: 1, page 97-123
  • ISSN: 0862-7940

Abstract

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We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three variables, i.e., the displacement, the pressure and the temperature. Lastly, we carry out numerical experiments to confirm the theoretical findings of our suggested approach.

How to cite

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Chen, Fan, Cui, Ming, and Zhou, Chenguang. "Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems." Applications of Mathematics (2025): 97-123. <http://eudml.org/doc/299924>.

@article{Chen2025,
abstract = {We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three variables, i.e., the displacement, the pressure and the temperature. Lastly, we carry out numerical experiments to confirm the theoretical findings of our suggested approach.},
author = {Chen, Fan, Cui, Ming, Zhou, Chenguang},
journal = {Applications of Mathematics},
keywords = {thermo-poroelasticity; fully implicit nonlinear discrete scheme; symmetric interior penalty discontinuous Galerkin method; a priori error estimate},
language = {eng},
number = {1},
pages = {97-123},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems},
url = {http://eudml.org/doc/299924},
year = {2025},
}

TY - JOUR
AU - Chen, Fan
AU - Cui, Ming
AU - Zhou, Chenguang
TI - Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 97
EP - 123
AB - We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three variables, i.e., the displacement, the pressure and the temperature. Lastly, we carry out numerical experiments to confirm the theoretical findings of our suggested approach.
LA - eng
KW - thermo-poroelasticity; fully implicit nonlinear discrete scheme; symmetric interior penalty discontinuous Galerkin method; a priori error estimate
UR - http://eudml.org/doc/299924
ER -

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