Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model

TL;DR

This paper develops and analyzes a robust discontinuous Galerkin method for simulating thermo/poro-viscoelastic problems, ensuring stability and accuracy across various physical parameters and complex geometries.

Contribution

It introduces an arbitrary-order weighted symmetric interior penalty scheme for Kelvin-Voigt thermo/poro-viscoelasticity, with comprehensive stability analysis and error estimates.

Findings

Method is stable for full inertial and quasi-static problems.

Supports general polytopal grids and heterogenous coefficients.

Numerical tests confirm convergence and robustness.

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 and we provide an a-priori error estimate. 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.