Mimetic spectral element method for anisotropic diffusion

Marc Gerritsma, Artur Palha, Varun Jain, Yi Zhang

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

This chapter addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulation is point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable; no stabilization is required and the method displays optimal convergence on orthogonal and deformed grids.

LanguageEnglish
Title of host publicationSEMA SIMAI Springer Series
EditorsD. Di Pietro, A. Ern, L. Formaggia
Place of PublicationCham
PublisherSpringer
Chapter3
Pages31-74
Number of pages44
ISBN (Electronic)978-3-319-94676-4
ISBN (Print)978-3-319-94675-7
DOIs
StatePublished - 1 Oct 2018

Publication series

NameSEMA SIMAI Springer Series
Volume15
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

Fingerprint

Spectral Element Method
Anisotropic Diffusion
Mixed Formulation
Incidence Matrix
Divergence-free
Diffusion Problem
Topological Structure
Sparse matrix
matrices
Differential operator
Stabilization
hands
Hand
differential operators
Grid
incidence
Metric
Dependent
Incidence
divergence

Cite this

Gerritsma, M., Palha, A., Jain, V., & Zhang, Y. (2018). Mimetic spectral element method for anisotropic diffusion. In D. Di Pietro, A. Ern, & L. Formaggia (Eds.), SEMA SIMAI Springer Series (pp. 31-74). (SEMA SIMAI Springer Series; Vol. 15). Cham: Springer. DOI: 10.1007/978-3-319-94676-4_3
Gerritsma, Marc ; Palha, Artur ; Jain, Varun ; Zhang, Yi. / Mimetic spectral element method for anisotropic diffusion. SEMA SIMAI Springer Series. editor / D. Di Pietro ; A. Ern ; L. Formaggia . Cham : Springer, 2018. pp. 31-74 (SEMA SIMAI Springer Series).
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Gerritsma, M, Palha, A, Jain, V & Zhang, Y 2018, Mimetic spectral element method for anisotropic diffusion. in D Di Pietro, A Ern & L Formaggia (eds), SEMA SIMAI Springer Series. SEMA SIMAI Springer Series, vol. 15, Springer, Cham, pp. 31-74. DOI: 10.1007/978-3-319-94676-4_3

Mimetic spectral element method for anisotropic diffusion. / Gerritsma, Marc; Palha, Artur; Jain, Varun; Zhang, Yi.

SEMA SIMAI Springer Series. ed. / D. Di Pietro; A. Ern; L. Formaggia . Cham : Springer, 2018. p. 31-74 (SEMA SIMAI Springer Series; Vol. 15).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Gerritsma M, Palha A, Jain V, Zhang Y. Mimetic spectral element method for anisotropic diffusion. In Di Pietro D, Ern A, Formaggia L, editors, SEMA SIMAI Springer Series. Cham: Springer. 2018. p. 31-74. (SEMA SIMAI Springer Series). Available from, DOI: 10.1007/978-3-319-94676-4_3