Optimal error estimates of the local discontinuous Galerkin method for nonlinear second‐order elliptic problems on Cartesian grids

ABSTRACT In this paper, we study the local discontinuous Galerkin (LDG) methods for two‐dimensional nonlinear second‐order elliptic problems of the type uxx + uyy = f(x, y, u, ux, uy), in a rectangular region Ω with classical boundary conditions on the boundary of Ω. Convergence properties for the s...

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Veröffentlicht in:	Numerical methods for partial differential equations 2021-01, Vol.37 (1), p.505-532
1. Verfasser:	Baccouch, Mahboub
Format:	Artikel
Sprache:	eng
Schlagworte:	a priori error estimates Boundary conditions Cartesian coordinates Convergence Dirichlet problem Exact solutions Galerkin method local discontinuous Galerkin method nonlinear second‐order elliptic boundary‐value problems Polynomials supercloseness Tensors
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