An adaptive stabilized finite element method for the Darcy’s equations with pressure dependent viscosities
Computer Methods in Applied Mechanics and Engineering(2021)
Abstract
This work aims to introduce and analyze an adaptive stabilized finite element method to solve a nonlinear Darcy equation with a 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 which confirm our theoretical results.
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Key words
Nonlinear Darcy’s equation,Stabilized finite element method,a priori error analysis,a posteriori error analysis
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