Interval boundary element method explained

Interval boundary element method is classical boundary element method with the interval parameters.
Boundary element method is based on the following integral equation

c ⋅ u = \int\limits _{\partial} \left(G (\partial u)/(\partial n) - (\partial G)/(\partial n) u\right)dS

The exact interval solution on the boundary can be defined in the following way:

\tilde{u}(x) = \{u(x,p):c(p) ⋅ u(p) = \int\limits _{\partial} \left(G(p) (\partial u(p))/(\partial n) - (\partial G(p))/(\partial n) u(p)\right)dS, p\in\hat{p} \}

In practice we are interested in the smallest interval which contain the exact solution set

\hat{u}(x) = hull \tilde {u}(x) = hull \{u(x,p):c(p) ⋅ u(p) = \int\limits _{\partial} \left(G(p) (\partial u(p))/(\partial n) - (\partial G(p))/(\partial n) u(p)\right)dS, p\in\hat{p} \}

In similar way it is possible to calculate the interval solution inside the boundary

\Omega .

See also

• Interval finite element

References

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