$H^1 $-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Spline Collocation Schemes for Elliptic Boundary Value Problems

Bernard Bialecki; Xiao-Chuan Cai

doi:10.1137/0731059

$H^1 $-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Spline Collocation Schemes for Elliptic Boundary Value Problems

SIAM Journal on Numerical Analysis ◽

10.1137/0731059 ◽

1994 ◽

Vol 31 (4) ◽

pp. 1128-1146 ◽

Cited By ~ 20

Author(s):

Bernard Bialecki ◽

Xiao-Chuan Cai

Keyword(s):

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Spline Collocation ◽

Elliptic Boundary Value ◽

Orthogonal Spline Collocation ◽

Norm Error

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Convergence Analysis of Orthogonal Spline Collocation for Elliptic Boundary Value Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142996305406 ◽

1998 ◽

Vol 35 (2) ◽

pp. 617-631 ◽

Cited By ~ 29

Author(s):

Bernard Bialecki

Keyword(s):

Boundary Value Problems ◽

Convergence Analysis ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Spline Collocation ◽

Elliptic Boundary Value ◽

Orthogonal Spline Collocation

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Matrix Decomposition Algorithms in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems

SIAM Journal on Scientific Computing ◽

10.1137/0916022 ◽

1995 ◽

Vol 16 (2) ◽

pp. 330-347 ◽

Cited By ~ 16

Author(s):

Bernard Bialecki ◽

Graeme Fairweather

Keyword(s):

Boundary Value Problems ◽

Elliptic Boundary ◽

Boundary Value ◽

Matrix Decomposition ◽

Elliptic Boundary Value Problems ◽

Decomposition Algorithms ◽

Spline Collocation ◽

Elliptic Boundary Value ◽

Orthogonal Spline Collocation ◽

Matrix Decomposition Algorithms

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Computable Error Bounds for the Finite Element Method for Elliptic Boundary Value Problems

Numerische Methoden bei Differentialgleichungen und mit funktionalanalytischen Hilfsmitteln - International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique ◽

10.1007/978-3-0348-6988-1_1 ◽

1974 ◽

pp. 9-27

Author(s):

R. E. Barnhill ◽

J. R. Whiteman

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

The Finite Element Method ◽

Elliptic Boundary Value ◽

Computable Error Bounds

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Estimated error bounds for finite element solutions of elliptic boundary value problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(95)00879-9 ◽

1996 ◽

Vol 130 (1-2) ◽

pp. 17-31 ◽

Cited By ~ 1

Author(s):

A. Mashaie ◽

E. Hughes ◽

J. Goldak

Keyword(s):

Finite Element ◽

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Estimated Error

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Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems

Symbolic Algebraic Methods and Verification Methods ◽

10.1007/978-3-7091-6280-4_19 ◽

2001 ◽

pp. 195-207 ◽

Cited By ~ 1

Author(s):

Michael Plum

Keyword(s):

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Numerical Error ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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Approximate Solution and Error Bounds for Quasi-Linear Elliptic Boundary Value Problems

SIAM Journal on Numerical Analysis ◽

10.1137/0707004 ◽

1970 ◽

Vol 7 (1) ◽

pp. 80-103 ◽

Cited By ~ 17

Author(s):

J. B. Rosen

Keyword(s):

Approximate Solution ◽

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Linear Elliptic Boundary

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Approximate solutions and error bounds for quasilinear elliptic boundary value problems

Journal of Computer and System Sciences ◽

10.1016/s0022-0000(73)80012-1 ◽

1973 ◽

Vol 7 (3) ◽

pp. 306-322 ◽

Cited By ~ 5

Author(s):

To-yat Cheung

Keyword(s):

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Approximate Solutions ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Quasilinear Elliptic

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Error bounds for finite element solutions of mildly nonlinear elliptic boundary value problems

Numerische Mathematik ◽

10.1007/bf01396570 ◽

1976 ◽

Vol 26 (1) ◽

pp. 107-116 ◽

Cited By ~ 16

Author(s):

M. A. Noor ◽

J. R. Whiteman

Keyword(s):

Finite Element ◽

Boundary Value Problems ◽

Error Bounds ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Nonlinear Elliptic ◽

Nonlinear Elliptic Boundary

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EXISTENCE OF COUPLED WEAK QUASI-SOLUTIONS OF SYSTEMS OF QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30195-4 ◽

1993 ◽

Vol 13 (1) ◽

pp. 102-110

Author(s):

Shixin Yang

Keyword(s):

Boundary Value Problems ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Quasilinear Elliptic

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Numerical solution of elliptic boundary-value problems for Schrödinger-type equations using the Kantorovich method

Mathematical Modelling and Geometry ◽

10.26456/mmg/2014-215 ◽

2014 ◽

Vol 2 (1) ◽

Author(s):

A.A. Gusev ◽

O. Chuluunbaatar ◽

S.I. Vinitsky ◽

A.G. Abrashkevich ◽

V.L. Derbov

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Kantorovich Method ◽

Elliptic Boundary Value

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