Year: 2025
Type: article
Abstract: The electroporoelasticity model, which couples Maxwell’s equations with Biot’s equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on investigating its well-posedness and analyzing error estimates for a splitting backward Euler finite element method. We first define a weak solution consistent with the finite element framework. Then, we prove the uniqueness and existence of such a solution using the Galerkin method and derive a priori estimates for high order regularity. Using a splitting technique, we define an splitting approximate solution and analyze its convergence order. Next, we apply Nédélec’s curl-conforming finite elements, Lagrange elements, and the backward Euler method to construct a fully discretized scheme. We demonstrate the stability of the splitting numerical solution and provide error estimates for its convergence order in both temporal and spatial variables. Finally, we present numerical experiments to validate the theoretical results, showing that our method significantly reduces computational complexity compared to the classical finite element method.
Source: Journal of Scientific Computing
Institutions: Jilin University, Auburn University, Southern Methodist University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4413446125