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Characterizing the inf-sup condition on product spaces

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Abstract

In this paper we establish characterization results for the continuous and discrete inf-sup conditions on product spaces. The inf-sup condition for each component of the bilinear form involved and suitable decompositions of the pivot space in terms of the associated null spaces are the key ingredients of our theorems. We illustrate the theory through its application to bilinear forms arising from the variational formulations of several boundary value problems.

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Authors and Affiliations

  1. CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Gabriel N. Gatica

  2. Departamento de Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, Marí a de Luna, 3 - 50018, Zaragoza, Spain

    Francisco-Javier Sayas

Authors
  1. Gabriel N. Gatica
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  2. Francisco-Javier Sayas
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Correspondence to Gabriel N. Gatica.

Additional information

Dedicated to Professor Ivo Babuska on the occasion of his 82nd birthday.

This research was partially supported by Centro de Modelamiento Matemático (CMM) of the Universidad de Chile, by Centro de Investigación en Ingenierí a Matemática (CI2MA) of the Universidad de Concepción, by FEDER/MCYT Project MTM2007-63204, and by Gobierno de Aragón (Grupo Consolidado PDIE).

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Gatica, G.N., Sayas, FJ. Characterizing the inf-sup condition on product spaces. Numer. Math. 109, 209–231 (2008). https://doi.org/10.1007/s00211-008-0140-3

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  • DOI: https://doi.org/10.1007/s00211-008-0140-3

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