Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
Optimal point placement for mesh smoothing
Journal of Algorithms
Algebraic Mesh Quality Metrics
SIAM Journal on Scientific Computing
A comparison of two optimization methods for mesh quality improvement
Engineering with Computers
An angle-based optimization approach for 2D finite element mesh smoothing
Finite Elements in Analysis and Design
The geometric element transformation method for mixed mesh smoothing
Engineering with Computers
Smoothing and local refinement techniques for improving tetrahedral mesh quality
Computers and Structures
Automatic merging of hexahedral meshes
Finite Elements in Analysis and Design
DARSS: a hybrid mesh smoother for all hexahedral meshes
Engineering with Computers
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Mesh quality plays an essential role in finite element applications, since it affects the efficiency of the simulation with respect to solution accuracy and computational effort. Therefore, mesh smoothing techniques are often applied for improving mesh quality while preserving mesh topology. One of these methods is the recently proposed geometric element transformation method (GETMe), which is based on regularizing element transformations. It will be shown numerically that this smoothing method is particularly suitable, from an applicational point of view, since it leads to a significant reduction of discretization errors within the first few smoothing steps requiring only little computational effort. Furthermore, due to reduced condition numbers of the stiffness matrices the performance of iterative solvers of the resulting finite element equations is improved. This is demonstrated for the Poisson equation with a number of meshes of different complexity and type as well as for piecewise linear and quadratic finite element basis functions. Results are compared to those obtained by two variants of Laplacian smoothing and a state of the art global optimization-based approach.