Discretely Compact Embeddings of Spaces of Cell-Centered Grid Functions

Abstract

Compactness of embeddings in discrete counterparts of Sobolev spaces is considered. We study the embeddings in spaces of cell-centered grid functions, in one- and two-dimensional domains. No restrictions are made on the mesh-ratios of the underlying meshes.

Keywords:

• Cell-centered grid functions
• Compactness
• Discrete spaces
• Embeddings

AMS Subject Classification:

• 46E39
• 74S20

ACKNOWLEDGMENTS

The research work compiled in this paper benefited from the suggestions of Rolf Dieter Grigorieff to whom the author wishes to express sincere gratitude. The author also thanks the helpful comments of José Augusto Ferreira and the paper reviewers.

The author gratefully acknowledges the support of this work by the Centro de Matemática da Universidade de Coimbra and Fundação para a Ciência e Tecnologia.