A local discontinuous Galerkin gradient discretization method for linear\n and quasilinear elliptic equations

2018/07/27 by Assyr Abdulle, Abdulle, Assyr, Giacomo Rosilho de Souza +1
Computer Science · Engineering · Mathematics · #65N15 #65N30 #65Y20 #74D10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1807.10645

openalex publication_date 2018/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A local weighted discontinuous Galerkin gradient discretization method for\nsolving elliptic equations is introduced. The local scheme is based on a coarse\ngrid and successively improves the solution solving a sequence of local\nelliptic problems in high gradient regions. Using the gradient discretization\nframework we prove convergence of the scheme for linear and quasilinear\nequations under minimal regularity assumptions. The error due to artificial\nboundary conditions is also analyzed, shown to be of higher order and shown to\ndepend only locally on the regularity of the solution. Numerical experiments\nillustrate our theoretical findings and the local method's accuracy is compared\nagainst the non local approach\n

Citations

• A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils

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