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

Research output: Contribution to journal › Article

5 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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Tabata, M. (1981). Conservative Upwind Finite Element Approximation and Its Applications. North-Holland Mathematics Studies, 47(C), 369-381. https://doi.org/10.1016/S0304-0208(08)71124-1

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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.",

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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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