Name
Title | ||
|---|---|---|
Defect-based local error estimators for high-order splitting methods involving three linear operators |
Abstract | ||
|---|---|---|
Prior work on high-order exponential operator splitting methods is extended to evolution equations defined by three linear operators. A posteriori local error estimators are constructed via a suitable integral representation of the local error involving the defect associated with the splitting solution and quadrature approximation via Hermite interpolation. In order to prove asymptotical correctness, a multiple integral representation involving iterated defects is deduced by repeated application of the variation-of-constant formula. The error analysis within the framework of abstract evolution equations provides the basis for concrete applications. Numerical examples for initial-boundary value problems of Schrödinger and of parabolic type confirm the asymptotical correctness of the proposed a posteriori error estimators. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s11075-014-9935-8 | Numerical Algorithms |
Keywords | Field | DocType |
Linear evolution equations,Time integration methods,High-order exponential operator splitting methods,Local error,A posteriori local error estimators,65J10,65L05,65M12,65M15 | Mathematical optimization,Exponential function,Mathematical analysis,A priori and a posteriori,Operator (computer programming),Quadrature (mathematics),Multiple integral,Hermite interpolation,Iterated function,Mathematics,Estimator | Journal |
Volume | Issue | ISSN |
70 | 1 | 1017-1398 |
Citations | PageRank | References |
3 | 0.43 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Winfried Auzinger | 1 | 56 | 10.48 |
| Othmar Koch | 2 | 174 | 28.41 |
| Mechthild Thalhammer | 3 | 124 | 16.02 |