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We propose a block-structured multigrid relaxation scheme for solving theStokes-Darcy Brinkman equations discretized by the marker and cell scheme. Anelement-based additive Vanka smoother is used to solve the correspondingshifted Laplacian operator. Using local Fourier analysis, we present thestencil for the additive Vanka smoother and derive an optimal smoothing factorfor Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkmanequations. Although the optimal damping parameter is dependent on meshsize andphysical parameter, it is very close to one. Numerical results of two-grid andV(1,1)-cycle are presented, which show high efficiency of the proposedrelaxation scheme and its robustness to physical parameters and the meshsize.Using a damping parameter equal to one gives almost the same results as thesefor the optimal damping parameter at a lower computational overhead.

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems