A mixed finite element method for fourth order partial differential equations. (English) Zbl 0616.73064
Für lineare Dirichletprobleme bei elliptischen Differentialgleichungen 4. Ordnung mit variablen Koeffizienten wird eine gemischte Finite- Element-Methode vorgestellt, die im Falle von Biegeproblemen bei elastischen Platten von variabler Dicke gleichzeitig Auslenkung, Krümmungskomponenten sowie Biege- und Torsionsmomente liefert. (Letztere erscheinen als Lagrangesche Multiplikatoren.) Unter passenden Regularitätsvoraussetzungen werden Fehlerabschätzungen gewonnen.
Reviewer: W.Velte
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74E10 | Anisotropy in solid mechanics |
| 74K20 | Plates |
Keywords:
mixed finite element solution; Dirichlet problem; fourth order elliptic linear partial differential operators; variable coefficients; bending problems; elastic plates; variable thickness; simultaneous determination of deflection, the curvature components and the actual bending and twisting moments; Lagrange multiplier; error estimates; regularity assumptions; Galerkin variational problemReferences:
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