Locking‐Free Mixed Interior Penalty DG Methods for the Total Pressure‐Formulation of the Biot‐Brinkman Model in Porous Media

ABSTRACT This work is devoted to overcome the locking phenomenon for the Biot‐Brinkman model, which describes the interaction between the deformation of a fluid‐saturated porous medium and viscous fluid flow. By introducing the total pressure in the Biot‐Brinkman equations, a four‐field formulation is derived as the target model. Well‐posedness is followed independent of the material parameters. The mixed interior penalty discontinuous Galerkin (IPDG) methods are used to derive stable numerical solutions. Error estimates in both –norm and energy norm are established, which show optimum for the SIPG scheme, and achieve parameter robustness in the case of . Numerical examples are provided to verify the accuracy and stability, as well as locking‐free of the proposed mixed DG methods.