Adaptive remeshing for compressible flow computations
Journal of Computational Physics
A mechanical model for a new grid generation method in computational fluid dynamics
Computer Methods in Applied Mechanics and Engineering
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
On adaptive grid refinement in the presence of internal or boundary layers
IMPACT of Computing in Science and Engineering
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
Jacobian-Weighted Elliptic Grid Generation
SIAM Journal on Scientific Computing
Delaunay mesh generation governed by metric specifications. Part I algorithms
Finite Elements in Analysis and Design
Delaunay mesh generation governed by metric specifications. Part II. applications
Finite Elements in Analysis and Design
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A monotone finite element scheme for convection-diffusion equations
Mathematics of Computation
Variational mesh adaptation: isotropy and equidistribution
Journal of Computational Physics
Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods
Journal of Computational Physics
Metric tensors for anisotropic mesh generation
Journal of Computational Physics
Modelling of heat transport in magnetised plasmas using non-aligned coordinates
Journal of Computational Physics
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Journal of Computational Physics
On discrete maximum principles for nonlinear elliptic problems
Mathematics and Computers in Simulation
Preserving monotonicity in anisotropic diffusion
Journal of Computational Physics
Journal of Computational Physics
A mixed implicit-explicit finite difference scheme for heat transport in magnetised plasmas
Journal of Computational Physics
Journal of Computational Physics
An anisotropic mesh adaptation method for the finite element solution of variational problems
Finite Elements in Analysis and Design
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.46 |
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.