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Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case

Abstract:

We develop a one-parameter family of hp-version discontinuous Galerkin finite element methods, parameterised by θ ∈ [-1, 1], for the numerical solution of quasilinear elliptic equations in divergence form on a bounded open set Ω ⊂ Rd, d ≥ 2. In particular, we consider the analysis of the family for the equation -∇ ·{μ(x, |∇u|)∇u} = f(x) subject to mixed Dirichlet-Neumann boundary conditions on ∂ Ω. It is assumed that μ is a real-valued function, μ ∈ C(Ω̄ × [0, ∞)), and there exist positive co...

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Publication status:
Published

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Publisher copy:
10.1093/imanum/dri014

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
IMA JOURNAL OF NUMERICAL ANALYSIS More from this journal
Volume:
25
Issue:
4
Pages:
726-749
Publication date:
2005-10-01
DOI:
EISSN:
1464-3642
ISSN:
0272-4979
Language:
English
Keywords:
Pubs id:
pubs:188323
UUID:
uuid:fdb215a6-ec51-41ed-a163-c1f77e50d1ef
Local pid:
pubs:188323
Source identifiers:
188323
Deposit date:
2012-12-19

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