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Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems
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Ortner, Christoph and Süli, Endre (2007) Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM Journal on Numerical Analysis, Volume 45 (Number 4). pp. 1370-1397. doi:10.1137/06067119X ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/06067119X
Abstract
We develop the convergence analysis of discontinuous Galerkin finite element approximations to symmetric second-order quasi-linear elliptic and hyperbolic systems of partial differential equations in divergence form in a bounded spatial domain in Rd, subject to mixed Dirichlet–Neumann boundary conditions. Optimal-order asymptotic bounds are derived on the discretization error in each case without requiring the global Lipschitz continuity or uniform monotonicity of the stress tensor. Instead, only local smoothness and a Gårding inequality are used in the analysis.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Galerkin methods, Finite element method, Convergence, Differential equations, Partial | ||||||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1429 | ||||||||
Official Date: | 11 July 2007 | ||||||||
Dates: |
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Volume: | Volume 45 | ||||||||
Number: | Number 4 | ||||||||
Page Range: | pp. 1370-1397 | ||||||||
DOI: | 10.1137/06067119X | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Funder: | European Union (EU) | ||||||||
Grant number: | HPRN-CT-2002-00284 (EU) |
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