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

Journal article

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, ...

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Authors: Ortner, C; Süli, E

• Publication status: Published
• Journal: SIAM J. Numerical Analysis
• Volume: 45
• Issue: 4
• Pages: 1370-1397
• Publication date: 2007-01-01
• DOI: 10.1137/06067119X
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: nonlinear elliptic and hyperbolic systems of partial differential equations; Legendre-Hadamard condition; broken Garding inequality; discontinuous Galerkin methods