Spectral element method for parabolic interface problems

Arbaz Khan; Chandra Shekhar Upadhyay; Marc Gerritsma

doi:10.1016/j.cma.2018.03.011

Spectral element method for parabolic interface problems

Arbaz Khan^*, Chandra Shekhar Upadhyay, Marc Gerritsma

^*Corresponding author for this work

Aerodynamics

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Abstract

In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.

Original language	English
Pages (from-to)	66-94
Number of pages	29
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	337
DOIs	https://doi.org/10.1016/j.cma.2018.03.011
Publication status	Published - 1 Aug 2018

Keywords

Least-squares method
Linear parabolic interface problems
Nonconforming
Sobolev spaces of different orders in space and time
Spectral element method

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10.1016/j.cma.2018.03.011

CMAME_D_17_01459Accepted author manuscript, 497 KBLicence: CC BY-NC-ND

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title = "Spectral element method for parabolic interface problems",

abstract = "In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.",

keywords = "Least-squares method, Linear parabolic interface problems, Nonconforming, Sobolev spaces of different orders in space and time, Spectral element method",

author = "Arbaz Khan and Upadhyay, {Chandra Shekhar} and Marc Gerritsma",

year = "2018",

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doi = "10.1016/j.cma.2018.03.011",

language = "English",

volume = "337",

pages = "66--94",

journal = "Computer Methods in Applied Mechanics and Engineering",

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TY - JOUR

T1 - Spectral element method for parabolic interface problems

AU - Khan, Arbaz

AU - Upadhyay, Chandra Shekhar

AU - Gerritsma, Marc

PY - 2018/8/1

Y1 - 2018/8/1

N2 - In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.

AB - In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.

KW - Least-squares method

KW - Linear parabolic interface problems

KW - Nonconforming

KW - Sobolev spaces of different orders in space and time

KW - Spectral element method

UR - http://www.scopus.com/inward/record.url?scp=85056297903&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.03.011

DO - 10.1016/j.cma.2018.03.011

M3 - Article

AN - SCOPUS:85056297903

SN - 0045-7825

VL - 337

SP - 66

EP - 94

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Spectral element method for parabolic interface problems

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