Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems.
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 condi...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2007
|
| Summary: | 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. © 2007 Society for Industrial and Applied Mathematics. |
|---|