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In this article, two kinds of local and parallel stabilized finite element methods based upon two grid discretizations are proposed and investigated for the Stokes–Darcy model. The lowest equal-order finite element pairs (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="bold">P</mi><mn>1</mn></msub></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mn>1</mn></msub></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mn>1</mn></msub></semantics></math></inline-formula>) are taken into account to approximate the velocity, pressure, and piezometric head, respectively. To circumvent the inf-sup condition, the stabilized term is chosen as the difference between a consistent and an under-integrated mass matrix. The proposed algorithms consist of approximating the low-frequency component on the global coarse grid and the high-frequency component on the local fine grid and assembling them to obtain the final approximation. To obtain a global continuous solution, the technique tool of the partition of unity is used. A rigorous theoretical analysis for the algorithms was conducted and numerical experiments were carried out to indicate the validity and efficiency of the algorithms.