Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model
Keywords
Advanced Numerical Methods for Scientific Computing
Geosciences/Protection of Land and Water Resources
Code:
101/2024
Title:
Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model
Date:
Friday 29th November 2024
Author(s):
Bonetti, S.; Corti, M.
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Abstract:
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model, and we develop a stability analysis in the continuous setting that holds both for the full inertial and quasi-static problems and that is robust with respect to most of the physical parameters of the problem. For spatial discretization, we propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. For the semi-discrete problem, we prove the extension of the stability result demonstrated in the continuous setting. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context.