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Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates

Chen, Goong / Zhou, Jianxin

Abstract Numerical solutions of nonlinear partial differential equations (PDEs) are important in applications. Historically, such work is done primarily by the finite differencemethods (FDM) and finite elementmethods (FEM).We note a few of such papers containing FDMand FEM numerical analysis of semilinear and quasilinear elliptic BVPs: Bers [17], Parter [155], Greenspan and Parter [83], for FDM; Ciarlet, Schultz and Varga [50], Dupont and Douglas [67], Brenner and Scott [28], for FEM.

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Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates

Chen, Goong / Zhou, Jianxin

Abstract Numerical solutions of nonlinear partial differential equations (PDEs) are important in applications. Historically, such work is done primarily by the finite differencemethods (FDM) and finite elementmethods (FEM).We note a few of such papers containing FDMand FEM numerical analysis of semilinear and quasilinear elliptic BVPs: Bers [17], Parter [155], Greenspan and Parter [83], for FDM; Ciarlet, Schultz and Varga [50], Dupont and Douglas [67], Brenner and Scott [28], for FEM.

Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates

Chen, Goong / Zhou, Jianxin

Abstract Numerical solutions of nonlinear partial differential equations (PDEs) are important in applications. Historically, such work is done primarily by the finite differencemethods (FDM) and finite elementmethods (FEM).We note a few of such papers containing FDMand FEM numerical analysis of semilinear and quasilinear elliptic BVPs: Bers [17], Parter [155], Greenspan and Parter [83], for FDM; Ciarlet, Schultz and Varga [50], Dupont and Douglas [67], Brenner and Scott [28], for FEM.

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Title:

Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates

Contributors:

Chen, Goong (author) / Zhou, Jianxin (author)

Published in:

Boundary Element Methods with Applications to Nonlinear Problems ; 545-612

Atlantis Studies in Mathematics for Engineering and Science ; 7

Publication date:

2010-01-01

Size:

68 pages

ISBN:

978-94-91216-27-5

ISSN:

DOI:

https://doi.org/10.2991/978-94-91216-27-5_11

Type of media:

Article/Chapter (Book)

Type of material:

Electronic Resource

Language:

English

Keywords:

Boundary Element , Nonlinear Problem , Boundary Element Method , Boundary Integral Equation , Robin Boundary Condition Mathematics , Operator Theory , Numerical Analysis

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