DeepAI AI Chat
Log In Sign Up

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

by   Weizhang Huang, et al.

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauss--Seidel (GS) method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.


page 20

page 22


A posteriori error estimates of finite element methods by preconditioning

We present a framework that relates preconditioning with a posteriori er...

Time-adaptive optimization in a parameter identification problem of HIV infection

The paper considers a time-adaptive method for determination of drug eff...

Scalable Recovery-based Adaptation on Quadtree Meshes for Advection-Diffusion-Reaction Problems

We propose a mesh adaptation procedure for Cartesian quadtree meshes, to...

Implicit adaptation of mesh model of transient heat conduction problem

Considering high-temperature heating, the equations of transient heat co...

Numerical Dissipation Based Error Estimators and Grid Adaptation for Large Eddy Simulation

Grid adaptation for implicit Large Eddy Simulation (LES) is a non-trivia...

Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg

This research note documents the integration of the MPI-parallel metric-...