Abstract
The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.
Highlights
The Finite Element Method (FEM) is a mature tool used to obtain the numerical solution of partial differential equations (PDEs) used in multiple engineering fields and physics [1,2,3,4]
We suggest to take the fundamental ideas from 2D refinement and apply them rigorously to the adaptivity with triangular prisms, solving the particularities that arise from the application of these ideas to volumetric meshes
There exist many different possibilities in the FEM community when choosing the shape of the finite element
Summary
The Finite Element Method (FEM) is a mature tool used to obtain the numerical solution of partial differential equations (PDEs) used in multiple engineering fields and physics [1,2,3,4]. Apart from the solid mathematical foundation of FEM, one of the main advantages of this technique is the use of adaptive refinement to improve the error convergence in the approximation of the field This leads to better use of the computational resources since we obtain automatically more accurate solutions with fewer unknowns to solve. In FEM, we can perform h refinements (decreasing the size of the elements used for discretizing the original domain) and p refinements (increasing the order of basis functions that approximate the field under study) The combination of these two refinements leads to the so-called hp refinement [5,6,7], which might lead to exponential convergence when appropriate estimators are used
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
