Error bounds in high-order Sobolev norms for POD expansions of parameterized transient temperatures |
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| Authors: | Mejdi Azaïez Faker Ben Belgacem Tomás Chacón Rebollo Macarena Gómez Mármol Isabel Sánchez Muñoz |
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| Institution: | 1. I2M, IPB (UMR CNRS 5295), Université de Bordeaux, 33607 Pessac, France;2. Sorbonne University, Université de technologie de Compiègne, LMAC Laboratory of Applied Mathematics of Compiègne, CS 60319, 60203 Compiègne cedex, France;3. Departamento de Ecuaciones Diferenciales y Análisis Numérico & Instituto de Matemáticas IMUS, Universidad de Sevilla, 41080 Sevilla, Spain;4. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, 41080 Sevilla, Spain;5. Departamento de Matemática Aplicada I, Universidad de Sevilla, 41013 Sevilla, Spain |
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| Abstract: | In this work, we analyze the convergence of the POD expansion for the solution to the heat conduction parameterized with respect to the thermal conductivity coefficient. We obtain error bounds for the POD approximation in high-order norms in space that assure an exponential rate of convergence, uniformly with respect to the parameter whenever it remains within a compact set of positive numbers. We present some numerical tests that confirm this theoretical accuracy. |
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