Analysis of least-squares approximations to second-order elliptic problems. II. Finite volume method

Suh Yuh Yang

doi:10.1081/NFA-120006703

Analysis of least-squares approximations to second-order elliptic problems. II. Finite volume method

Suh Yuh Yang

Department of Mathematics

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

1 Scopus citations

Abstract

A theoretical analysis of the combined finite volume/least squares approximations to boundary value problems for second-order elliptic equations in mixed first-order system formulation with variable coefficients in two- and three-dimensional bounded domains is presented. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the finite volume discretization process is achieved. An optimal error estimate in the H¹(Ω) product norm for continuous piecewise linear approximating function spaces is derived. An equivalent a posteriori error estimator in the H¹(Ω) product norm is also proposed and analyzed.

Original language	English
Pages (from-to)	433-451
Number of pages	19
Journal	Numerical Functional Analysis and Optimization
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1081/NFA-120006703
State	Published - May 2002

Keywords

A posteriori error estimates
A priori error estimates
Elliptic problems
Finite volume methods
Least squares

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10.1081/NFA-120006703

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abstract = "A theoretical analysis of the combined finite volume/least squares approximations to boundary value problems for second-order elliptic equations in mixed first-order system formulation with variable coefficients in two- and three-dimensional bounded domains is presented. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the finite volume discretization process is achieved. An optimal error estimate in the H1(Ω) product norm for continuous piecewise linear approximating function spaces is derived. An equivalent a posteriori error estimator in the H1(Ω) product norm is also proposed and analyzed.",

keywords = "A posteriori error estimates, A priori error estimates, Elliptic problems, Finite volume methods, Least squares",

author = "Yang, {Suh Yuh}",

note = "Funding Information: This work was supported in part by the National Science Council of Taiwan under grants NSC 89-2115-M-214-002 and NSC 89-2115-M-008-030.",

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AU - Yang, Suh Yuh

N1 - Funding Information: This work was supported in part by the National Science Council of Taiwan under grants NSC 89-2115-M-214-002 and NSC 89-2115-M-008-030.

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Y1 - 2002/5

N2 - A theoretical analysis of the combined finite volume/least squares approximations to boundary value problems for second-order elliptic equations in mixed first-order system formulation with variable coefficients in two- and three-dimensional bounded domains is presented. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the finite volume discretization process is achieved. An optimal error estimate in the H1(Ω) product norm for continuous piecewise linear approximating function spaces is derived. An equivalent a posteriori error estimator in the H1(Ω) product norm is also proposed and analyzed.

AB - A theoretical analysis of the combined finite volume/least squares approximations to boundary value problems for second-order elliptic equations in mixed first-order system formulation with variable coefficients in two- and three-dimensional bounded domains is presented. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the finite volume discretization process is achieved. An optimal error estimate in the H1(Ω) product norm for continuous piecewise linear approximating function spaces is derived. An equivalent a posteriori error estimator in the H1(Ω) product norm is also proposed and analyzed.

KW - A posteriori error estimates

KW - A priori error estimates

KW - Elliptic problems

KW - Finite volume methods

KW - Least squares

UR - http://www.scopus.com/inward/record.url?scp=0036578679&partnerID=8YFLogxK

U2 - 10.1081/NFA-120006703

DO - 10.1081/NFA-120006703

M3 - 期刊論文

AN - SCOPUS:0036578679

SN - 0163-0563

VL - 23

SP - 433

EP - 451

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 3-4

ER -

Analysis of least-squares approximations to second-order elliptic problems. II. Finite volume method

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Keywords

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