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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 for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p.
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- Publisher:
- Unspecified
- Publication date:
- 2004-06-01
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- UUID:
-
uuid:6f6ed566-9809-4147-be98-bf7856aa58e9
- Local pid:
- oai:eprints.maths.ox.ac.uk:1176
- Deposit date:
- 2011-05-20
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- Copyright date:
- 2004
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