Defect-correction multigrid methods for nonlinear problems |
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| Institution: | 1. Department of Mathematics, Tufts University, Medford, MA 02155, USA;2. School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310058, China;3. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA;1. Helmut Schmidt University, Faculty of Mechanical and Civil Engineering, Holstenhofweg 85, 22043 Hamburg, Germany;2. University of Bergen, Department of Mathematics, Center for Modeling of Coupled Subsurface Dynamics, Allegaten 41, 50520 Bergen, Norway;1. Research Center for Applied Mathematics and Machine Intelligence, Zhejiang Lab, Hangzhou 311121, China;2. Research Center for Mathematics, Beijing Normal University, Zhuhai 519087, China;3. Guangdong Key Laboratory of IRADS, BNU-HKBU United International College, Zhuhai 519087, China;4. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;5. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China |
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| Abstract: | Auzinger and Stetter 1] combine a multigrid method with defect-correction iteration and derive a composite iterative procedure which they call the DCMG (defect-correction multigrid) cycle. Using a high-order discrete operator in the coarsegrid correction and a lower-order operator in relaxation, the DCMG cycle achieves the higher-order approximation 4]. In an analogous way, DCMG can be used to solve nonlinear PDEs by using the nonlinear operator in correction and a related linear operator in relaxation. We prove convergence of such a DCMG scheme and give an error estimation. |
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