Different mesh management strategies for non-stationary self-adaptive hp finite element method

Maciej Paszyński¹, Paweł Matuszyk²

¹Department of Computer Science, AGH University of Science and Technology Al. Mickiewicza 30, 30-059 Cracow, Poland.
²Department of Applied Computer Science and Modelling, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland.

DOI:

https://doi.org/10.7494/cmms.2010.1.0276

Abstract:

In this paper we compare different strategies for solving non-stationary heat and mass transfer problems, utilized to simulate austenite-ferrite phase transformation. The self-adaptive hp Finite Element Method (hp-FEM) is utilized to solve the heat and mass transfer problems at every time step. The hp-FEM generates a sequence of hp refined meshes delivering exponential convergence of the numerical error with respect to mesh size. To solve the computational problem at every time step, the hp-FEM utilizes the numerical solution from previous time step. We compare three different techniques for utilization of the previous time step solution. The first one generates a new mesh for the next time step starting from the regular initial mesh, the second one utilizes previous time step computational mesh, and the third one performs some unrefinements on the mesh from the previous time step before solving the actual time step. The comparison is based on the numerical simulation of the austenite-ferrite phase transition phenomena.

Cite as:

Paszyński, M., & Matuszyk, P. (2010). Different mesh management strategies for non-stationary self-adaptive hp finite element method. Computer Methods in Materials Science, 10(1), 42 – 51. https://doi.org/10.7494/cmms.2010.1.0276

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