A new family of mixed finite elements in IR3
Numerische Mathematik
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
A Posteriori Error Estimators for the Raviart--Thomas Element
SIAM Journal on Numerical Analysis
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
A posteriori error indicators for Maxwell's equations
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods
SIAM Review
A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions
SIAM Journal on Numerical Analysis
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
SIAM Journal on Numerical Analysis
Auxiliary space preconditioning in H0(curl; Ω)
Numerische Mathematik
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
An Adaptive Multilevel Method for Time-Harmonic Maxwell Equations with Singularities
SIAM Journal on Scientific Computing
Linear Convergence of an Adaptive Finite Element Method for the $p$-Laplacian Equation
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
An adaptive edge finite element method for electromagnetic cloaking simulation
Journal of Computational Physics
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An efficient and reliable a posteriori error estimate is derived for solving three-dimensional static Maxwell's equations by using the edge elements of first family. Based on the a posteriori error estimates, an adaptive finite element method is constructed and its convergence is established. Compared with the existing results, an important advantage of the new theory lies in its feature that the usual marking of elements based on the oscillation is not needed in our adaptive algorithm, while the linear convergence of the algorithm can be still demonstrated in terms of the reduction of the energy-norm error and the oscillation. Numerical examples are provided which demonstrate the effectiveness and robustness of the adaptive methods.