Volume 1, Issue 4
Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods

Qiya Hu

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 383-409.

Published online: 2008-01

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  • Abstract

A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied. It is shown that the new normal-like derivatives, which are called the generalized normal derivatives, preserve the major properties of the existing standard normal derivatives. The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order elliptic problems. The approximate solutions generated by these methods still possess the optimal energy-norm error estimates, even if the exact solutions to the underlying elliptic problems admit very low regularities.

  • Keywords

Green's formula, generalized normal derivative, domain decomposition, nonmathing grids, discontinuous Galerkin, error estimates.

  • AMS Subject Headings

46E35, 65M15, 65M55, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-383, author = {}, title = {Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {4}, pages = {383--409}, abstract = {

A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied. It is shown that the new normal-like derivatives, which are called the generalized normal derivatives, preserve the major properties of the existing standard normal derivatives. The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order elliptic problems. The approximate solutions generated by these methods still possess the optimal energy-norm error estimates, even if the exact solutions to the underlying elliptic problems admit very low regularities.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6056.html} }
TY - JOUR T1 - Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 383 EP - 409 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6056.html KW - Green's formula, generalized normal derivative, domain decomposition, nonmathing grids, discontinuous Galerkin, error estimates. AB -

A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied. It is shown that the new normal-like derivatives, which are called the generalized normal derivatives, preserve the major properties of the existing standard normal derivatives. The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order elliptic problems. The approximate solutions generated by these methods still possess the optimal energy-norm error estimates, even if the exact solutions to the underlying elliptic problems admit very low regularities.

Qiya Hu. (2020). Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods. Numerical Mathematics: Theory, Methods and Applications. 1 (4). 383-409. doi:
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