Multipatch Discontinuous Galerkin IGA for the Biharmonic Problem On Surfaces

12/07/2020 ∙ by Stephen E. Moore, et al. ∙ 0

We present the analysis of interior penalty discontinuous Galerkin Isogeometric Analysis (dGIGA) for the biharmonic problem on orientable surfaces Ω⊂ℝ^3. Here, we consider a surface consisting of several non-overlapping patches as typical in multipatch dGIGA. Due to the non-overlapping nature of the patches, we construct NURBS approximation spaces which are discontinuous across the patch interfaces via a penalty scheme. By an appropriate discrete norm, we present a priori error estimates for the non-symmetric, symmetric and semi-symmetric interior penalty methods. Finally, we confirm our theoritical results with numerical experiments.

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