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Hessian 2D remeshing

Author: Vicente Mataix Ferrándiz

Kratos version: 7.1

Source files: Hessian 2D

Case Specification

In this test case,

The following applications of Kratos are used:

  • MeshingApplication with the MMG module

The problem corresponds with the example proposed in reference. The objective is to remesh the following structured mesh of a domain 1x1:

Debore remesh

Where the size of the elements is very small and the distribution of the elements is not the optimal to represent the following test function:

Error function

The challenge consists in using the Hessian function of the test function as error measure and adapt the mesh in a proper manner.


The results obtained after remeshing can be see in the following figures:


The color map of the test function:


The variation of the element size:

Nodal H


Frédéric Alauzet. Metric-Based Anisotropic Mesh Adaptation. Course material, CEA-EDF-INRIA Schools. Numerical Analysis Summer School.

Pascal Tremblay 2-D, 3-D and 4-D Anisotropic Mesh Adaptation for the Time-Continuous Space-Time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations. PhD thesis Ottawa-Carleton Institute for Mechanical and Aerospace Engineering, Department of Mechanical Engineering, University of Ottawa. 2007.

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