Conservative Upwind Finite Element Approximation and Its Applications

Masahisa Tabata

doi:10.1016/S0304-0208(08)71124-1

Conservative Upwind Finite Element Approximation and Its Applications

Masahisa Tabata^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We present a finite element approximation which is effective for diffusion problems with dominated non-linear convection terms. This approximation is conservative and of upwind type. We analyse it in connection with L² -theory, L¹ -contraction and monotonicity. As an application we consider a non-linear elliptic problem and give error analysis. In the process the existence of the exact solution is also proved.

Original language	English
Pages (from-to)	369-381
Number of pages	13
Journal	North-Holland Mathematics Studies
Volume	47
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)71124-1
Publication status	Published - 1981
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1016/S0304-0208(08)71124-1

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title = "Conservative Upwind Finite Element Approximation and Its Applications",

abstract = "We present a finite element approximation which is effective for diffusion problems with dominated non-linear convection terms. This approximation is conservative and of upwind type. We analyse it in connection with L2 -theory, L1 -contraction and monotonicity. As an application we consider a non-linear elliptic problem and give error analysis. In the process the existence of the exact solution is also proved.",

author = "Masahisa Tabata",

year = "1981",

doi = "10.1016/S0304-0208(08)71124-1",

language = "English",

volume = "47",

pages = "369--381",

journal = "North-Holland Mathematics Studies",

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number = "C",

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T1 - Conservative Upwind Finite Element Approximation and Its Applications

AU - Tabata, Masahisa

PY - 1981

Y1 - 1981

N2 - We present a finite element approximation which is effective for diffusion problems with dominated non-linear convection terms. This approximation is conservative and of upwind type. We analyse it in connection with L2 -theory, L1 -contraction and monotonicity. As an application we consider a non-linear elliptic problem and give error analysis. In the process the existence of the exact solution is also proved.

AB - We present a finite element approximation which is effective for diffusion problems with dominated non-linear convection terms. This approximation is conservative and of upwind type. We analyse it in connection with L2 -theory, L1 -contraction and monotonicity. As an application we consider a non-linear elliptic problem and give error analysis. In the process the existence of the exact solution is also proved.

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U2 - 10.1016/S0304-0208(08)71124-1

DO - 10.1016/S0304-0208(08)71124-1

M3 - Article

AN - SCOPUS:77956915554

VL - 47

SP - 369

EP - 381

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

SN - 0304-0208

IS - C

ER -

Conservative Upwind Finite Element Approximation and Its Applications

Abstract

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