The three R's of engineering analysis and error estimation and adaptivity
Computer Methods in Applied Mechanics and Engineering
Journal of Computational and Applied Mathematics
Bucking analysis: alternative formulations, error estimation, and adaptive meshing
Finite Elements in Analysis and Design
Efficient error estimation and adaptive meshing method for boundary element analysis
Advances in Engineering Software
The superconvergent patch recovery (SPR) and adaptive finite element refinement
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Superconvergence and the superconvergent patch recovery
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh Medal Competition
Adaptive refinement of unstructured finite-element meshes
Finite Elements in Analysis and Design
Variational mesh adaptation II: error estimates and monitor functions
Journal of Computational Physics
Anisotropic finite elements for the Stokes problem: a posteriori error estimator and adaptive mesh
Journal of Computational and Applied Mathematics
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
A nearest-nodes finite element method with local multivariate Lagrange interpolation
Finite Elements in Analysis and Design
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In this paper, an adaptive finite element method is formulated based on the newly developed nearest-nodes finite element method (NN-FEM). In the adaptive NN-FEM, mesh modification is guided by the gradient of strain energy density, i.e., a larger gradient requires a denser mesh and vice versa. A finite element mesh is iteratively modified by a set of operators, including mesh refinement, mesh coarsening and mesh smoothing, to make its density conform the gradient of strain energy density. The selection of a proper operator for a specific mesh region is determined by a set of criteria based on mesh intensity. The iteration loop of mesh modification is stopped when the relative error in the total potential energy is less than a prescribed accuracy. Numerical examples are presented to demonstrate the performance of the proposed adaptive NN-FEM.