T(x) giuen a∈r 1imx-∞T(x)=0 where Q is the infinite domain outside the square and r is the region formed by he edges of the square. Using finite-element or finite-difference methods to solve this problem requires introducing an additional approximation beyond discretization error. It is not possible to discretize all of Q, as it is infinite, and therefore the domain must be truncated with an artificial finite boundary. In the slide, the artificial boundary a large ellipse on which we assume the temperature is zero. Clearly, as the radius of the ellipse increases, the truncated problem more accurately represents the domain problem, but the number of unknowns in the discretization increases.T (x) given x ∈ Γ lim
x
→∞T (x)=0 where Ω is the infinite domain outside the square and Γ is the region formed by the edges of the square. Using finite-element or finite-difference methods to solve this problem requires introducing an additional approximation beyond discretization error. It is not possible to discretize all of Ω, as it is infinite, and therefore the domain must be truncated with an artificial finite boundary. In the slide,the artificial boundary is a large ellipse on which we assume the temperature is zero. Clearly, as the radius of the ellipse increases, the truncated problem more accurately represents the domain problem, but the number of unknowns in the discretization increases. 6