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Number 2593
Author Debrabant, Kristian
Jakobsen, Espen R.
Title Semi-Lagrangian schemes for linear and fully non-linear diffusion equations
Upload 6.10.2009
MSC 65M12
65M15
65M06
35K10
35K55
35K65
49L25
49L20
ZDM N40
CR G.1.m
PACS 02.60.Cb
Keywords Monotone approximation schemes
difference-interpolation methods
stability
convergence
error bound
degenerate parabolic equations
Hamilton-Jacobi-Bellman equations
viscosity solution

Abstract:
 For linear and fully non-linear diffusion equations of
  Bellman-Isaacs type, we introduce a class of monotone approximation
  schemes relying on monotone interpolation. As opposed to classical
  numerical methods, these schemes converge for degenerate diffusion
  equations having general non-diagonal dominant coefficient matrices.
  Such schemes have to have a wide stencil in general.  Besides
  providing a unifying framework for several known first order
  accurate schemes, our class of schemes also includes more efficient versions,
  and a new second order scheme that converges only for
  essentially monotone solutions.  The methods are easy to implement
  and analyze, and they are more efficient than some other known
  schemes. We prove stability and convergence of the schemes in the
  general case, and provide error estimates in the convex case
  which are robust in the sense that they apply to degenerate equations
  and non-smooth solutions.  The methods are extensively tested.

File:
DebrabantJakobsen1Preprint.pdf

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