L1-Based Approximations of PDEs and Applications

Abstract

The objective of this project was to develop robust numerical methods for solving mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems, advection-dominated flows, multiphase flows, and free-boundary problems, where shocks, fronts, and contact discontinuities are driving features and pose significant difficulties for traditional numerical methods. The main thrust of this research program was to explain some intriguing numerical observations reported by Lavery, Jiang, and Guermond [4]1 that seemed to indicate that for some classes of PDE s equipped with non-smooth coefficients and/or non-smooth right-hand sides it pays off to approximate the solution directly in L1. Contrary to standard stabilized L2-based techniques, L1-based methods did not seem to require additional ad hoc tunable coefficients or limiting procedures.

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Document Details

Document Type
Technical Report
Publication Date
Sep 05, 2012
Accession Number
ADA577117

Entities

People

  • Bojan Popov
  • Jean-luc Guermond

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boltzmann Equation
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Digital Elevation Models
  • Discontinuities
  • Equations
  • Fluid Dynamics
  • Images
  • Students
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design