The Well-Posedness and Numerical Analysis of the Differential Variational-Hemivariational Inequalities Arising from the Double-Diffusive Convection Problem

<jats:p>This study explores the mathematical model of double-diffusive convection phenomena occurring when fluids pass through porous media. The mixed boundary conditions for the velocity field are considered, and both convex subdifferential and Clarke subdifferential are taken into account. The variational form constitutes a coupled system consisting of a variational-hemivariational inequality for the velocity field and two ordinary parabolic differential equations for temperature field and solute concentration field. We analyze the well-posedness of the solution to this nonlinear inequality system and derive the error estimate. Under appropriate solution regularity assumptions, the optimal error estimate of the numerical solution is derived.</jats:p>