Design and data structure of fully adaptive, multigrid, finite-element software
ACM Transactions on Mathematical Software (TOMS)
On the multi-level splitting of finite element spaces
Numerische Mathematik
On the abstract theory of additive and multiplicative Schwarz algorithms
Numerische Mathematik
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Load Balancing for Adaptive Multigrid Methods
SIAM Journal on Scientific Computing
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Multigrid Methods on Adaptively Refined Grids
Computing in Science and Engineering
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
Mathematics and Computers in Simulation
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
Data structures and requirements for hp finite element software
ACM Transactions on Mathematical Software (TOMS)
A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
SIAM Journal on Scientific Computing
An efficient linear elastic FEM solver using automatic local grid refinement and accuracy control
Finite Elements in Analysis and Design
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A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library.