A high-order HDG method for the Biot's consolidation model
Guosheng Fu
TL;DR
This paper introduces a high-order hybridizable discontinuous Galerkin (HDG) method for solving the Biot's consolidation model in poroelasticity, with proven optimal error estimates and validated through numerical experiments.
Contribution
The paper develops a new high-order HDG scheme for Biot's model, including comprehensive error analysis and numerical validation, advancing numerical methods in poroelasticity.
Findings
Optimal error estimates for semi-discrete and full-discrete schemes
Numerical tests confirm the method's accuracy and efficiency
The method outperforms existing approaches in convergence and stability
Abstract
We propose a novel high-order HDG method for the Biot's consolidation model in poroelasticity. We present optimal error analysis for both the semi-discrete and full-discrete (combined with temporal backward differentiation formula) schemes. Numerical tests are provided to demonstrate the performance of the method.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods · Numerical methods in engineering