Volume 7, Issue 4
Max-Norm Estimates for Galerkin Approximations of One-Dimensional Elliptic, Parabolic and Hyperbolic Problems with Mixed Boundary Conditions

Che Sun

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J. Comp. Math., 7 (1989), pp. 383-396

Published online: 1989-07

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  • Abstract

The Galerkin methods are studied for two-point boundary value problems and the related one-dimensional parabolic and hyperbolic problems. The boundary value problem considered here is of non-adjoint from and with mixed boundary conditions. The optimal order error estimate in the max-norm is first derived for the boundary problem for the finite element subspace. This result then gives optimal order max-norm error estimates for the continuous and discrete time approximations for the evolution problems described above.

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@Article{JCM-7-383, author = {}, title = {Max-Norm Estimates for Galerkin Approximations of One-Dimensional Elliptic, Parabolic and Hyperbolic Problems with Mixed Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {4}, pages = {383--396}, abstract = { The Galerkin methods are studied for two-point boundary value problems and the related one-dimensional parabolic and hyperbolic problems. The boundary value problem considered here is of non-adjoint from and with mixed boundary conditions. The optimal order error estimate in the max-norm is first derived for the boundary problem for the finite element subspace. This result then gives optimal order max-norm error estimates for the continuous and discrete time approximations for the evolution problems described above. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9488.html} }
TY - JOUR T1 - Max-Norm Estimates for Galerkin Approximations of One-Dimensional Elliptic, Parabolic and Hyperbolic Problems with Mixed Boundary Conditions JO - Journal of Computational Mathematics VL - 4 SP - 383 EP - 396 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9488.html KW - AB - The Galerkin methods are studied for two-point boundary value problems and the related one-dimensional parabolic and hyperbolic problems. The boundary value problem considered here is of non-adjoint from and with mixed boundary conditions. The optimal order error estimate in the max-norm is first derived for the boundary problem for the finite element subspace. This result then gives optimal order max-norm error estimates for the continuous and discrete time approximations for the evolution problems described above.
Che Sun. (1970). Max-Norm Estimates for Galerkin Approximations of One-Dimensional Elliptic, Parabolic and Hyperbolic Problems with Mixed Boundary Conditions. Journal of Computational Mathematics. 7 (4). 383-396. doi:
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