Name
Title | ||
|---|---|---|
A posteriori error analysis for a class of integral equations and variational inequalities |
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s00211-010-0310-y | Numerische Mathematik |
Keywords | Field | DocType |
local error,posteriori error estimator,particular pure jump process,actual error,posteriori error analysis,adaptive algorithm,implicit euler method,american option,time estimator,diffusion process,variational inequality,discrete non-contact region,integral equation,upper bound,differential operators,piecewise linear,finite element | Discretization,Mathematical optimization,Mathematical analysis,Jump diffusion,Finite element method,Numerical analysis,Backward Euler method,Piecewise linear function,Mathematics,Estimator,Variational inequality | Journal |
Volume | Issue | ISSN |
116 | 3 | 0945-3245 |
Citations | PageRank | References |
11 | 0.70 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ricardo H. Nochetto | 1 | 907 | 110.08 |
| Tobias von Petersdorff | 2 | 12 | 1.09 |
| Chen-song Zhang | 3 | 34 | 5.92 |