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diffuse interface approximation of Dirichlet problem for the Poisson equation. A slice of u(x,y) along y = 0 for different values of ε as labeled. [a]: result using Approximation 1 in equation (2.21), [b]: result using Approximation 2 in equation (2.22) and [c]: result using Approximation 3 in equation (2.23).
