We present the analysis of interior penalty discontinuous Galerkin Isogeometric Analysis (dGIGA) for the biharmonic problem on orientable surfaces $\Omega \subset \mathbb{R}^3.$ 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 \textit{a priori} error estimates for the non-symmetric, symmetric and semi-symmetric interior penalty methods. Finally, we confirm our theoritical results with numerical experiments.
翻译:我们在此对可调整表面的双声调问题加热尔金同位素分析(dGIGA)进行内部处罚不连续分析。 这里,我们认为由多个非重叠补丁构成的表面是多式dGIGA中常见的。 由于补丁的不重叠性质,我们建造了NURBS近似空间,这些空间通过一种惩罚办法在补丁界面之间互不相连。根据适当的离散规范,我们提出非对称、对称和半对称内部处罚方法的误差估计。最后,我们用数字实验来确认我们的实验结果。