On the numerical analysis of non-convex variational problems |
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Authors: | Pablo Pedregal |
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Affiliation: | (1) Departamento de Matemática Aplicada, Universidad Complutense de Madrid, E-28040 Madrid, Spain , ES |
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Abstract: | Summary. We discuss a numerical method for finding Young-measure-valued minimizers of non-convex variational problems. To have any hope of a convergence theorem, one must work in a setting where the minimizer is unique and minimizing sequences converge strongly. This paper has two main goals: (i) we specify a method for producing strongly-convergent minimizing sequences, despite the failure of strict convexity; and (ii) we show how uniqueness of the Young measure can be parlayed into a numerical convergence theorem. The treatment of (ii) is done in the setting of two model problems, one involving scalar valued functions and a multiwell energy, the other from micromagnetics. Received July 29, 1995 |
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Keywords: | Mathematics Subject Classification (1991):65K10 |
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