Error estimators for nonconforming finite element approximations of the Stokes problem
Mathematics of Computation
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
A unifying theory of a posteriori error control for nonconforming finite element methods
Numerische Mathematik
An Optimal Adaptive Finite Element Method for the Stokes Problem
SIAM Journal on Numerical Analysis
An optimally convergent adaptive mixed finite element method
Numerische Mathematik
Convergence of a standard adaptive nonconforming finite element method with optimal complexity
Applied Numerical Mathematics
A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Journal of Scientific Computing
Computers & Mathematics with Applications
| Hi-index | 0.00 |
We prove convergence and quasi-optimal complexity of adaptive nonconforming low-order finite element methods for the Stokes equations, covering the Crouzeix-Raviart discretization on triangular and tetrahedral meshes, as well as the Rannacher-Turek discretization on two- and three-dimensional rectangular meshes. Hanging nodes are allowed in order to ease local mesh refinement. The adaptive algorithm is based on standard a posteriori error estimators consisting of two parts: a volume residual and an edge term measuring the nonconformity of the velocity approximation. We use an adaptive marking strategies, which, in each step of the iteration, takes only the dominant term into account. This paper can be regarded as an extension of [R. Becker, S. Mao, and Z.-C. Shi, SIAM J. Numer. Anal., 47 (2010), pp. 4639-4659] to the Stokes problem, but the analysis here does not make use of any relationship between mixed and nonconforming finite element methods.