Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
Error equidistribution and mesh adaptation
SIAM Journal on Scientific Computing
Grid adaption based on modified anisotropic diffusion equations formulated in the parametric domain
Journal of Computational Physics
Mesh generation using vector-fields
Journal of Computational Physics
Jacobian-Weighted Elliptic Grid Generation
SIAM Journal on Scientific Computing
Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems
SIAM Journal on Numerical Analysis
A Framework for Variational Grid Generation: Conditioning the Jacobian Matrix with Matrix Norms
SIAM Journal on Scientific Computing
Practical aspects of formulation and solution of moving mesh partial differential equations
Journal of Computational Physics
Variational mesh adaptation: isotropy and equidistribution
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Grid Generation Methods
Applied Numerical Mathematics
Approaches for generating moving adaptive meshes: location versus velocity
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
r-Adaptive mesh generation for shell finite element analysis
Journal of Computational Physics
Moving mesh methods with locally varying time steps
Journal of Computational Physics
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations
Journal of Computational Physics
Journal of Computational Physics
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
Adaptive nearest-nodes finite element method guided by gradient of linear strain energy density
Finite Elements in Analysis and Design
Exact asymptotics of the uniform error of interpolation by multilinear splines
Journal of Approximation Theory
Journal of Computational Physics
A numerical study of air-vapor-heat transport through textile materials with a moving interface
Journal of Computational and Applied Mathematics
Hi-index | 31.49 |
The key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation. In this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work [J. Comput. Phys. 174 (2001) 924]. Two types of monitor functions, scalar matrix and non-scalar matrix ones, are defined based on asymptotic estimates of interpolation error obtained using the interpolation theory of finite element methods. The choice of the adaptation intensity parameter is also discussed for each of these monitor functions. Asymptotic bounds on interpolation error are obtained for adaptive meshes that satisfy the regularity and equidistribution conditions. Two-dimensional numerical results are given to verify the theoretical findings.