Numerical solutions of the m-membranes problem |
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Institution: | 1. Department of Mathematics and Statistics, Arkansas State University, State University, Arkansas, USA;2. Department of Mathematics, University of California, Irvine, CA USA;3. Department of Computational Science and Engineering, Yonsei University, Seoul 03722, South Korea |
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Abstract: | In this paper numerical approximation for the m-membrane problem is considered. We make a change of variables that leads to a different expression of the quadratic functional that allows after discretizing the problem to reformulate it as finite dimensional bound constrained quadratic problem. To our knowledge this is the first paper on numerical approximation of the m-membrane problem. We reformulate the m-membrane problem as a bound constraint quadratic minimization problem. The bound constraint quadratic form is solved with the gradient projection method. |
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