| Abstract: |
| We develop and analyze a RBF meshless Galerkin method for elliptic Dirichlet boundary control problems on smooth curved domains. The method is posed on the exact curved domain and imposes the inhomogeneous Dirichlet boundary condition weakly by a Nitsche-type formulation. This avoids the geometric errors introduced when curved boundaries are approximated by polynomial boundary-fitted meshes. Using Bernstein inequalities for kernel-based trial spaces, we derive kernel-based inverse and trace estimates tailored to this boundary control setting. These estimates allow us to prove the stability and optimal error estimates of the proposed method. Numerical experiments on smooth domains with curved boundaries confirm the theoretical convergence rates. The approach can also provides a basis for extensions to curved interface problems, in particular to multi-domain coupled problems with curved interfaces. |
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