Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations

Brittany Froese Hamfeldt, Tiago Salvador

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring consistency, monotonicity, and convergence. We describe an algorithm for efficiently computing the non-traditional finite difference stencils. We also present a strategy for computing formally higher-order convergent methods. Computational examples demonstrate the efficiency, accuracy, and flexibility of the methods.

Original languageEnglish (US)
Pages (from-to)1282-1306
Number of pages25
JournalJournal of Scientific Computing
Volume75
Issue number3
DOIs
StatePublished - Jun 1 2018

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Adaptive methods
  • Finite difference methods
  • Fully nonlinear elliptic partial differential equations
  • Higher-order methods

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