Analysis of mixed discontinuous Galerkin formulations for quasilinear elliptic problems

2017/02/09 by Mohammad Zakerzadeh, Zakerzadeh, Mohammad, Georg May +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1702.02733

openalex publication_date 2017/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this manuscript we present an approach to analyze the discontinuous Galerkin solution for general quasilinear elliptic problems. This approach is sufficiently general to extend most of the well-known discretization schemes, including BR1, BR2, SIPG and LDG, to nonlinear cases in a canonical way, and to establish the stability of their solution. Furthermore, in case of monotone and globally Lipschitz problems, we prove the existence and uniqueness of the approximated solution and the h-optimality of the error estimate in the energy norm as well as in the L₂ norm.

Citations

• A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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