Efficiency of high‐order elements for continuous and discontinuous Galerkin methods. (16th July 2013)

• Record Type: Journal Article
• Authors: Huerta, Antonio; Angeloski, Aleksandar; Roca, Xevi; Peraire, Jaime
• Is Part Of: International journal for numerical methods in engineering. Volume 96:Number 9(2013)
• Page Start: 529
• Page End: 560
• Publication Date: 2013-07-16
• Subjects: high‐order elements -- efficiency -- work estimates -- computational cost; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4547
• Languages: English
• ISSNs: 0029-5981

Abstract

SUMMARY: To evaluate the computational performance of high‐order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high‐order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two‐dimensional and three‐dimensional domains for simplices and parallelotopes. Moreover, both element‐wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high‐order methods are more efficient than linear ones. Copyright © 2013 John Wiley & Sons, Ltd.