Analysis of Domain Embedding Method for Elliptic Problems Defined Over Curved Complex Domains
Solving Partial differential equations over curved complex domains is a very challenging job due to the meshing intricacy of the domain. In particular, for time-dependent problems, meshing is needed at each time step if the domain has a moving interface, which increases the computational cost intensely. So, we insert the given domain into a more extensive rectangular domain and use the structured triangular grid and linear finite element method to solve the extended penalized version of the given partial differential equation over a rectangular domain. Penalty parameters are used to utilize the original boundary conditions. The a priori estimates and stability results are derived for the proposed idea with the error estimates in H1 and L2 norms. Error analysis ensures the practical applications of the method, and several numerical experiments demonstrate the theoretical results.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.