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Pre-Publicación 2020-28

Rodolfo Araya, Cristian Cárcamo, Abner Poza:

An adaptive stabilized finite element method for the Darcy’s equations with pressure dependent viscosities

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 wellposedness 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 threedimensional numerical examples which confirm our theoretical results.

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