Upwind difference approximations for degenerate parabolic convection–diffusion equations with a discontinuous coefficient

By Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, John D. Towers. 2002

120 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7c4808005b82b4c18640dc2786a860927a02221e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Kenneth Hvistendahl Karlsen
2. Nils Henrik Risebro
3. Florence Bachmann
4. Julien Vovelle
5. John D. Towers
6. Evgeny Yu. Panov

In Computational Theory and Mathematics

1. Kenneth Hvistendahl Karlsen
2. Nils Henrik Risebro
3. John D. Towers
4. Julien Vovelle
5. Gui-Qiang G. Chen
6. Mario Ohlberger
7. Raimund Bürger
8. Timothy J. Barth

In Numerical Analysis

1. Kenneth Hvistendahl Karlsen
2. Nils Henrik Risebro
3. John D. Towers

Citations in the corpus

• Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients (2006, background): “It has been proven in different works (Bachmann, 2004; Karlsen and Risebro, 2001; Karlsen et al., 2002b; Seguin and Vovelle, 2003; Towers, 2000) that this notion of entropy solution allows to show that existence, uniqueness, consistence with approximations holds.”
• OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS (2005, unknown): “They use regularization of coefficients as in [18], via the Hamilton–Jacobi equation and regularization of coefficients as in [31], some are based on front tracking as in [14, 24, 23, 10] while others used numerical schemes of the Godunov or Enquist–Osher type as in [34, 35, 19 , 9] and of the Lax–”
• ON A NONLINEAR DEGENERATE PARABOLIC TRANSPORT-DIFFUSION EQUATION WITH A DISCONTINUOUS COEFFICIENT (2002, methodology): “Here we derive instead strong convergence via a series of a priori (energy) estimates that allow us to deduce convergence of the diffusion function and use the compensated compactness method to deal with the transport term.”
• CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX (2004, background): “We refer to introductory parts of [12, 13] for an overview of the activity on problems with discontinuous fluxes.”
• ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS (2003, unknown): “[6, 7, 18, 19, 20], we let γ(x) := vmax(x) and rewrite the conservation law (1.”