A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem
Provides theoretical guarantees for adaptive mesh refinement in Stokes flow, which is important for computational fluid dynamics.
The paper proves contraction and quasi-optimal complexity for an adaptive divergence-conforming discontinuous Galerkin method for the Stokes problem, reducing velocity error.
We prove the contraction property for two successive loops of the adaptive algorithm for the Stokes problem reducing the error of the velocity. The problem is discretized by a divergence-conforming discontinuous Galerkin method which separates pressure and velocity approximation due to its cochain property. This allows us to establish the quasi-orthogonality property which is crucial for the proof of the contraction. We also establish the quasi-optimal complexity of the adaptive algorithm in terms of the degrees of freedom.