Abstract
This paper investigates the application of the generalized finite element method with global-local enrichments (GFEMgl) to problems of transient heat transfer involving localized features. The GFEMgl is utilized in order to numerically construct general, specially-tailored shape functions yielding high levels of accuracy on coarse FEM meshes. The use of time-dependent shape functions requires that the system of equations be discretized temporally first, and then spatially in order to properly account for the time-dependency. The standard α-method is used for the time integration scheme. The transient three-dimensional GFEMgl is then applied to a laser heating example in order to demonstrate its ability to resolve localized, transient features on a fixed, coarse mesh. Convergence analysis of the proposed method as well as applications to heterogeneous materials, and moving heat sources are also provided.
Original language | English (US) |
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Pages (from-to) | 812-829 |
Number of pages | 18 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 200 |
Issue number | 5-8 |
DOIs | |
State | Published - Jan 15 2011 |
Keywords
- Generalized finite elements
- Global local finite elements
- Hp methods
- Multiscale problems
- Rough solutions
- Transient analysis
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications