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A stable and accurate relaxation technique using multiple penalty terms in space and time
Affiliation:1. Heat and Mass Transfer Technological Center, Polytechnical University of Catalonia, TR4 Building, 11th Colon Str., 08222 Terrassa (Barcelona), Spain;2. TermoFluids S. L., 97-E Jacquard Av., 08222 Terrassa (Barcelona), Spain;1. Department of Applied Mathematics, Naval Postgraduate School, 833 Dyer Road, Monterey, CA 93943–5216, United States of America;2. Department of Mathematics, Southern Methodist University, PO Box 750156, Dallas, TX 75275–0156, United States of America;3. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, United States of America;1. Department of Basic Sciences, School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Campus H-12, 44000 Islamabad, Pakistan;2. DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa;3. School of Natural Sciences, National University of Sciences and Technology, Campus H-12, 44000 Islamabad, Pakistan;1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;2. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China
Abstract:A new method for data relaxation based on weak imposition of external data is introduced. The technique is simple, easy to implement, and the resulting numerical scheme is unconditionally stable. Numerical experiments show that the error growth naturally present in long term simulations can be prevented by using the new technique.
Keywords:Data relaxation  Data assimilation  Summation-by-parts  Weak boundary conditions  Multiple penalties  Stability  Finite differences
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