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	An averaging scheme for macroscopic numerical simulation of nonconvex minimization problems
	Li, Zhi-Ping ; Carstensen, Carsten
	2007
关键词	averaging scheme nonconvex minimization convexification macroscopic numerical simulation adaptive mesh refinement POSTERIORI ERROR CONTROL ONE CONVEX ENVELOPES MESH TRANSFORMATION METHOD FINITE-ELEMENT METHODS COMPUTING MICROSTRUCTURES PART I COMPUTATION ELASTICITY FEM MINIMIZERS
英文摘要	Averaging or gradient recovery techniques, which are a popular tool for improved convergence or superconvergence of finite element methods in elliptic partial differential equations, have not been recommended for nonconvex minimization problems as the energy minimization process enforces finer and finer oscillations and hence at the first glance, a smoothing step appears even counterproductive. For macroscopic quantities such as the stress field, however, this counterargument is no longer true. In fact, this paper advertises an averaging technique for a surprisingly improved convergence behavior for nonconvex minimization problems. Similar to a finite volume scheme, numerical experiments on a double-well benchmark example provide empirical evidence of superconvergence phenomena in macroscopic numerical simulations of oscillating microstructures.; Computer Science, Software Engineering; Mathematics, Applied; SCI(E); 0; ARTICLE; 3; 601-611; 47
语种	英语
出处	SCI
出版者	bit numerical mathematics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/249731]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li, Zhi-Ping,Carstensen, Carsten. An averaging scheme for macroscopic numerical simulation of nonconvex minimization problems. 2007-01-01.

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