A numerical method for singularly perturbed elliptic problems posed on domains with a curved boundary

Key Points

• The proposed numerical method effectively addresses singular perturbation in elliptic problems, improving solution validity.
• Key performance metrics reveal that the method achieves higher accuracy rates than previous techniques, particularly on curved boundaries.
• Analysis of numerical simulations show promising outcomes when applied to various boundary conditions across multiple test scenarios.
• Implications indicate the need for further exploration in higher dimensions, given the initial success in two-dimensional cases.