Interior maximum-norm estimates for finite element methods, part II
Mathematics of Computation
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
A two-grid discretization scheme for eigenvalue problems
Mathematics of Computation
Convergence of Adaptive Finite Element Methods
SIAM Review
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
SIAM Journal on Numerical Analysis
A Defect Correction Scheme for Finite Element Eigenvalues with Applications to Quantum Chemistry
SIAM Journal on Scientific Computing
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
Three-Scale Finite Element Discretizations for Quantum Eigenvalue Problems
SIAM Journal on Numerical Analysis
Adaptive eigenvalue computation: complexity estimates
Numerische Mathematik
Convergence and optimal complexity of adaptive finite element eigenvalue computations
Numerische Mathematik
Advances in Computational Mathematics
SIAM Journal on Numerical Analysis
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In this paper, adaptive finite element methods for differential operator eigenvalue problems are discussed. For multi-scale discretization schemes based on Rayleigh quotient iteration (see Scheme 3 in [Y. Yang, H. Bi, A two-grid discretization scheme based on shifted-inverse power method, SIAM J. Numer. Anal. 49 (2011) 1602-1624]), a reliable and efficient a posteriori error indicator is given, in addition, a new adaptive algorithm based on the multi-scale discretizations is proposed, and we apply the algorithm to the Schrodinger equation for hydrogen atoms. The algorithm is performed under the package of Chen, and satisfactory numerical results are obtained.