A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem (Journal of Mathematical Study, 2014)
In this paper, we carry out an a posteriori error analysis of Legendre spectralapproximations to the Stokes/Darcy coupled equations. The spectral approximationsare based on a weak formulation of the coupled equations by using the Beavers-Joseph-Saffman interface condition. The main contribution of the paper consists of derivinga number of posteriori error indicators and their upper and lower bounds for the single domain case. An extension of the upper bounds to the multi-domain case in thespectral element framework is also given.
Keywords: A posteriori error; Stokes/Darcy coupled equations; Spectral method; Spectral element method.