An immersed interface method for a 1D poroelasticity problem with discontinuous coefficients

We introduce an immersed interface method (IIM) based on a staggered grid for the 1D Biot’s poroelasticity model when the coefficients have discontinuities along material interfaces. The IIM uses a standard finite difference method away from the interfaces and modifies the numerical schemes near or on the interfaces to treat the irregularities using the method of undetermined coefficients. A second-order accuracy in the infinity norm has been derived for both pressure and displacement regardless of the position of the interfaces. We present some numerical results to confirm the theoretical error estimates.