Convergence analysis of all-at-once multigrid methods for elliptic control problems under partial elliptic regularity (Q2845615)
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scientific article; zbMATH DE number 6203700
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence analysis of all-at-once multigrid methods for elliptic control problems under partial elliptic regularity |
scientific article; zbMATH DE number 6203700 |
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2 September 2013
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PDE-constrained optimization
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all-at-once multigrid methods
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reduced regularity
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convergence
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distributed optimal control problem
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Convergence analysis of all-at-once multigrid methods for elliptic control problems under partial elliptic regularity (English)
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The authors consider the convergence theory for an all-at-once multigrid method for the following distributed optimal control problem NEWLINE\[NEWLINEJ(y, u)={1\over 2}\| y- y_D\|^2_{L^2(\Omega)}+{\alpha\over 2}\| u\|^2_{L^2(\Omega)},NEWLINE\]NEWLINE NEWLINE\[NEWLINE-\Delta y+ y= u\quad\text{and}\quad {\partial y\over\partial n}= 0\quad\text{on}\quad \partial\Omega.NEWLINE\]NEWLINE The authors give a new proof which is based on a more straightforward approach.
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