Title: An a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in Karst aquifers: anisotropic and isotropic discretizations,
Abstract: This paper presents an a posteriori error analysis for a coupled continuum
pipe-flow/Darcy model in karst aquifers. We consider a unified anisotropic
finite element discretization (i.e. elements with very large aspect ratio). Our
analysis covers two-dimensional domains, conforming and nonconforming
discretizations as well as different elements. Many examples of finite elements
that are covered by analysis are presented. From the finite element solution,
the error estimators are constructed and based on the residual of model
equations. Lower and upper error bounds form the main result with minimal
assumptions on the elements. The lower error bound is uniform with respect to
the mesh anisotropy in the entire domain. The upper error bound depends on a
proper alignment of the anisotropy of the mesh which is a common feature of
anisotropic error estimation. In the special case of isotropic meshes, the
results simplify, and upper and lower error bounds hold unconditionally.