An adaptive stabilized finite element method for Darcy’s equations with pressure-dependent viscosities
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This work aims to introduce and analyze an adaptive stabilized finite element method to solve a nonlinear Darcy equation with pressure-dependent viscosity and mixed boundary conditions. We stated the discrete problem’s well-posedness and optimal error estimates in natural norms under standard assumptions. Next, we introduce and analyze a residual-based a posteriori error estimator for the stabilized scheme. Finally, we present some two- and three-dimensional numerical examples that confirm our theoretical results.