Locking-Free Finite Element Approximation to 3D Quasi-Static Electroporoelasticity Equations

Le résumé fourni par la source

The mathematical model of electroporoelasticity is comprised of Maxwell's equations coupled to Biot's equations. Numerical approximations may exhibit Poisson locking when the Lamé constant is large and the exact solution's divergence is small. In this paper, we propose a locking-free finite element method for approximating solutions, derive error estimates and show first-order convergence (which are independent of the Lamé constant). It is shown that the proposed numerical method inherits its asymptotic behavior from the original equations, ensuring that the algorithm is locking-free. We present numerical experiments that illustrate our theoretical findings.

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