Mixed Finite Element Methods for Problems with Robin Boundary Conditions

We derive new a priori and a posteriori error estimates for mixed finite element discretizations of second-order elliptic problems with general Robin boundary conditions, parameterized by $\varepsilon\geq0$. The estimates are robust in $\varepsilon$, ranging from pure Dirichlet conditions to pure Neumann conditions. We also show that hybridization leads to a well-conditioned linear system. A series of numerical experiments is presented that verify our theoretical results.

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