Robust A Posteriori Error Analysis for Rotation-Based Formulations of the Elasticity/Poroelasticity Coupling

We develop the a posteriori error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretizations use $H^1$-conforming elements degree $k+1$ displacement fluid pressure, discontinuous piecewise polynomials $k$ rotation vector, total elastic pressure. Residual-based estimators are constructed, upper lower bounds (up to data oscillations) all global rigorously derived. methods robust with respect model parameters (in particular, Lamé constants); they valid 2D 3D, also arbitrary polynomial $k\geq 0$. behavior predicted by theoretical is then demonstrated numerically on set computational examples including different geometries which we perform adaptive mesh refinement guided estimators.