CORNERS GIVE PROBLEMS WHEN DECOUPLING FOURTH ORDER EQUATIONS INTO SECOND ORDER SYSTEMS
Decoupling a fourth order elliptic boundary value problem into a system of second order equations may give an alternative approach to obtaining a solution for the original problem. The system approach is usually preferred for numerical methods since one may use piecewise linear finite elements to ap...
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Veröffentlicht in: | SIAM journal on numerical analysis 2012-01, Vol.50 (3), p.1604-1623 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Decoupling a fourth order elliptic boundary value problem into a system of second order equations may give an alternative approach to obtaining a solution for the original problem. The system approach is usually preferred for numerical methods since one may use piecewise linear finite elements to approximate a solution. In this note we compare both settings for the plate equation and prove that for planar domains with corners the system approach may fail to produce the correct solution. |
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ISSN: | 0036-1429 1095-7170 |
DOI: | 10.1137/100806151 |