Dr. Poza-Diaz, Abner

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Dr. Poza-Diaz, Abner
Nombre completo
Poza Diaz, Abner Haguit
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apoza@ucsc.cl
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Author: Cárcamo, Cristian × Subject: A priori error analysis ×

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    Publication
    An adaptive stabilized finite element method for the Darcy's equations with pressure dependent viscosities
    (Computer Methods in Applied Mechanics and Engineering, 2021)
    Dr. Poza-Diaz, Abner 
    ;
    Araya, Rodolfo
    ;
    Cárcamo, Cristian
    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.