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Dual Consistency and Output Superconvergence



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Dual Consistency and Output Superconvergence Huafei Sun and Masayuki Yano Massachusetts Institute of Technology Department of Aeronautics and Astronautics May 13 2009 H Sun M Yano MIT 16 930 Video Project May 13 2009 1 15 Problem Statement Model Equation The Poisson equation in 0 1 R1 with Dirichlet B C u xx f in u x 0 u x 1 0 for some f L2 Output of Interest Z J u gudx u x x 0 for some g L2 H Sun M Yano MIT 16 930 Video Project May 13 2009 2 15 Problem Statement Model Equation The Poisson equation in 0 1 R1 with Dirichlet B C u xx f in u x 0 u x 1 0 for some f L2 Output of Interest Z J u gudx u x x 0 for some g L2 H Sun M Yano MIT 16 930 Video Project May 13 2009 2 15 Dual Consistency Primal Continuous Primal Dual Dualize Continuous Dual Discretize Discretize Discrete Primal True Discrete Dual TDD Dualize Discrete Dual DD Dual Consistency Discrete dual problem is consistent discretization of continuous dual problem i e DD TDD H Sun M Yano MIT 16 930 Video Project May 13 2009 3 15 Dual Consistency Primal Continuous Primal Dual Dualize Continuous Dual Discretize Discretize Discrete Primal True Discrete Dual TDD Dualize Discrete Dual DD Dual Consistency Discrete dual problem is consistent discretization of continuous dual problem i e DD TDD H Sun M Yano MIT 16 930 Video Project May 13 2009 3 15 Dual Consistency Primal Continuous Primal Dual Dualize Continuous Dual Discretize Discretize Discrete Primal True Discrete Dual TDD Dualize Discrete Dual DD Dual Consistency Discrete dual problem is consistent discretization of continuous dual problem i e DD TDD H Sun M Yano MIT 16 930 Video Project May 13 2009 3 15 Dual Consistency Primal Continuous Primal Dual Dualize Continuous Dual Discretize Discretize Discrete Primal True Discrete Dual TDD Dualize Discrete Dual DD Dual Consistency Discrete dual problem is consistent discretization of continuous dual problem i e DD TDD H Sun M Yano MIT 16 930 Video Project May 13 2009 3 15 Map of the Primal World Primal Continuous Primal



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