Mimetic Spectral Element Method for Anisotropic Diffusion

Marc Gerritsma; Artur Palha; Varun Jain; Yi Zhang

doi:10.1007/978-3-319-94676-4_3

Mimetic Spectral Element Method for Anisotropic Diffusion

Marc Gerritsma^*, Artur Palha, Varun Jain, Yi Zhang

^*Corresponding author for this work

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

7 Citations (Scopus)

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.

Original language	English
Title of host publication	SEMA SIMAI Springer Series
Editors	Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia
Publisher	Springer
Pages	31-74
Number of pages	44
Volume	15
ISBN (Electronic)	978-3-319-94676-4
ISBN (Print)	978-3-319-94675-7
DOIs	https://doi.org/10.1007/978-3-319-94676-4_3
Publication status	Published - 1 Jan 2018

Publication series

Name	SEMA SIMAI Springer Series
Volume	15
ISSN (Print)	2199-3041
ISSN (Electronic)	2199-305X

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10.1007/978-3-319-94676-4_3

Cite this

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Mimetic Spectral Element Method for Anisotropic Diffusion. / Gerritsma, Marc ; Palha, Artur; Jain, Varun et al.
SEMA SIMAI Springer Series. ed. / Daniele Antonio Di Pietro; Alexandre Ern; Luca Formaggia. Vol. 15 Springer, 2018. p. 31-74 (SEMA SIMAI Springer Series; Vol. 15).

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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T1 - Mimetic Spectral Element Method for Anisotropic Diffusion

AU - Gerritsma, Marc

AU - Palha, Artur

AU - Jain, Varun

AU - Zhang, Yi

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Y1 - 2018/1/1

N2 - 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.

AB - 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.

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SN - 978-3-319-94675-7

VL - 15

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A2 - Di Pietro, Daniele Antonio

A2 - Ern, Alexandre

A2 - Formaggia, Luca

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ER -

Mimetic Spectral Element Method for Anisotropic Diffusion

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Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency

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