A posteriori error analysis for a class of integral equations and variational inequalities

  • Authors:

  • Ricardo H. Nochetto;Tobias von Petersdorff;Chen-Song Zhang

  • Affiliations:

  • University of Maryland, Department of Mathematics, Institute of Physical Science and Technology, 20742, College Park, MD, USA;University of Maryland, Department of Mathematics, 20742, College Park, MD, USA;Penn State University, Department of Mathematics, 16802, State College, PA, USA

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order $${2s \in (0,2]}$$. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes or jump diffusion processes with tempered stable processes. The problem is discretized using piecewise linear finite elements in space and the implicit Euler method in time. We construct a residual-type a posteriori error estimator which gives a computable upper bound for the actual error in H s -norm. The estimator is localized in the sense that the residuals are restricted to the discrete non-contact region. Numerical experiments illustrate the accuracy of the space and time estimators, and show that they can be used to measure local errors and drive adaptive algorithms.