Isogeometric analysis: Approximation, stability and error estimates for \(h\)-refined meshes. (English) Zbl 1103.65113
Approximation and stability properties of nonuniform rational B-splines are studied. Applications to elasticity, Stokes flow and advection-diffusion and numerical tests are given.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D07 | Numerical computation using splines |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
Keywords:
B-splines; NURBS; finite elements; error estimates; stability; elliptic boundary value problems; elasticity; Stokes flow; advection-diffusion equation; \(h\)-refinement; numerical examples; non-uniform rational B-splinesReferences:
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