To solve the inverse Cauchy problem in linear elasticity by a novel Lie-group integrator

Figures & data

Figure 1. For example 1 by applying the GPS to integrate the governing equations with $\mathit{\alpha }=-2$ leads to unstable solutions.

Figure 2. For example 1 comparing the recovered displacements and tractions with exact ones on the top side.

Figure 3. For example 1 comparing the numerical errors of recovered displacements on the top side with $\mathit{\alpha }=-1$, and $\mathit{\alpha }=0$.

Figure 4. For example 1 comparing the numerical errors of displacements and the Neumann data on the top side with different $\mathit{\alpha }$.

Figure 5. For example 1 with ${\mathit{\eta }}_1$ and ${\mathit{\eta }}_2$ alternating, comparing the numerical solutions with exact ones.

Figure 6. For example 2 comparing the recovered displacements and tractions with exact ones on the top side.

Figure 7. For example 3 comparing the recovered displacements and the Neumann data with exact ones on the top side.

Figure 8. For example 4 comparing the recovered displacements and tractions with exact ones on the top side.

Figure 9. For example 4 comparing the numerical errors of displacements and the Neumann data on the top side with different $\mathit{\alpha }$.

Figure 10. The inverse Cauchy problem to recover data on ${\mathrm{\Gamma }}_2$.

Figure 11. For example 5 comparing numerical and exact solutions of the inverse Cauchy problem for Laplace equation.

Figure 12. For example 6 of a nonlinear inverse Cauchy problem of elasticity, comparing the recovered displacements and the Neumann data with exact ones on the top side.

Figure 13. For example 7 of a nonlinear inverse Cauchy problem of elasticity, comparing the recovered displacements with exact ones on the top side.