A Mixed Formulation for the Fractional Poisson Problem
DOI:
https://doi.org/10.70567/mc.v41i15.77Keywords:
Fractional laplacian, mixed formulation, finite element methodAbstract
The mixed formulation of the classical Poisson problem consists in the introduction of a
flux as a new variable with adequate boundary conditions, resulting in a system of coupled equation system.
Using fractional calculus identities, in this work we explore a mixed formulation of the fractional
Poisson problem and prove the well-posedness of the problem. A direct discretization of this problem
seems out of reach, by following Hughes and Masud we are able to introduce a stabilized formulation
that results in a coercive and well-posed problem. The coercivity implies that any confirming finite element
discretization is stable. Lastly, we prove the convergence of this discretization and discuss its
implementations.
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