Burman Erik, Hansbo Peter, Larson Mats G, Larsson Karl, Massing André
1Department of Mathematics, University College London, London, WC1E 6BT UK.
2Department of Mechanical Engineering, Jönköping University, 55111 Jönköping, Sweden.
Numer Math (Heidelb). 2019;141(1):141-172. doi: 10.1007/s00211-018-0990-2. Epub 2018 Jul 14.
We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order in the energy and norms that take the approximation of the surface and the boundary into account.
我们针对具有边界和非齐次狄利克雷边界条件的曲面上的拉普拉斯 - 贝尔特拉米算子开发了一种有限元方法。该方法基于曲面的三角剖分，并且使用尼茨方法弱施加边界条件。我们证明了对于考虑曲面和边界逼近的能量范数和 范数下的 阶分段连续多项式，具有最优阶的先验误差估计。
