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Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems

Abstract:

We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, $-\sum_{\alpha=1}^d \partial_{x_\alpha} S_{i\alpha}(\nabla u(x)) = f_i(x)$, $i=1,\dots, d$, and $\partial^2_t{u}_i-\sum_{\alpha=1}^d \partial_{x_\alpha} S_{i\alpha}(\nabla u(t,x)) = f_i(t,x)$, $i=1,\dots, d$, with $\partial_{x_\alpha} = \partial/\partial x_\alpha$, in a bounded spati...

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Publication date:
2006-05-05
URN:
uuid:7b96ae31-5d6c-4cc7-90e2-2e3a07e63822
Local pid:
oai:eprints.maths.ox.ac.uk:1118

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