A Mixed Virtual Element Method for the p-Laplace Equation
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In this talk, we present a Mixed Virtual Element method for the numerical approximation of the mixed formulation of the nonlinear p-Laplace equation. A specific stabilization term is introduced, designed to capture the monotonicity and boundedness properties of the continuous nonlinear diffusion operator. This stabilization is thoroughly analyzed and theoretically investigated. We also provide a complete well-posedness result, based on the discrete inf-sup condition, as well as a priori estimates that demonstrate the convergence rates of the proposed method. Finally, we conclude with a set of numerical experiments that validate the theoretical findings.
