Design and data structure of fully adaptive, multigrid, finite-element software
ACM Transactions on Mathematical Software (TOMS)
Analysis of a Finite Element Method--PDE/PROTRAN
Analysis of a Finite Element Method--PDE/PROTRAN
Adaptive Projection Operators in Multiresolution Scientific Visualization
IEEE Transactions on Visualization and Computer Graphics
Adaptive Projection Operators in Multiresolution Scientific Visualization
IEEE Transactions on Visualization and Computer Graphics
Parallel Adaptive Mesh Refinement with Load Balancing for Finite Element Method
PaCT '01 Proceedings of the 6th International Conference on Parallel Computing Technologies
A general purpose adaptivity driver for FE software
Software—Practice & Experience
Spacetime meshing with adaptive refinement and coarsening
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The 8-tetrahedra longest-edge partition of right-type tetrahedra
Finite Elements in Analysis and Design
Non-degeneracy study of the 8-tetrahedra longest-edge partition
Applied Numerical Mathematics
A comparative study between some bisection based partitions in 3D
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
An adaptive mixed finite element method for wind field adjustment
Advances in Engineering Software
Adaptive spacetime meshing for discontinuous Galerkin methods
Computational Geometry: Theory and Applications
An automatic strategy for adaptive tetrahedral mesh generation
Applied Numerical Mathematics
Non-degeneracy study of the 8-tetrahedra longest-edge partition
Applied Numerical Mathematics
A comparative study between some bisection based partitions in 3D
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
The 8-tetrahedra longest-edge partition of right-type tetrahedra
Finite Elements in Analysis and Design
Convergence of a standard adaptive nonconforming finite element method with optimal complexity
Applied Numerical Mathematics
Adaptive meshless centres and RBF stencils for Poisson equation
Journal of Computational Physics
A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Convergence of an Adaptive Mixed Finite Element Method for Kirchhoff Plate Bending Problems
SIAM Journal on Numerical Analysis
3D Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
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Adaptive refinement has proved to be a useful tool for reducing the size of the linear system of equations obtained by discretizing partial differential equations. We consider techniques for the adaptive refinement of triangulations used with the finite element method with piecewise linear functions. Several such techniques that differ mainly in the method for dividing triangles and the method for indicating which triangles have the largest error have been developed. We describe four methods for dividing triangles and eight methods for indicating errors. Angle bounds for the triangle division methods are compared. All combinations of triangle divisions and error indicators are compared in a numerical experiment using a population of eight test problems with a variety of difficulties (peaks, boundary layers, singularities, etc.). The comparison is based on the L-infinity norm of the error versus the number of vertices. It is found that all of the methods produce asymptotically optimal grids and that the number of vertices needed for a given error rarely differs by more than a factor of two.