## On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation.(English)Zbl 1185.65171

This paper is near in its problem, assumptions, regularization method and result to that of H.-H. Qin and T. Wei [Math. Comput. Simul. 80, No. 2, 352–366 (2009; Zbl 1185.65172)] who, however, considered the modified Helmholtz equation and also a second regularization method – proving better in the numerical experiments.
These authors obtain $$L_2$$ convergence of the regularized solution choosing the regularization parameter in dependence on solution apriori bound and measurement error, but show no numerical results.

### MSC:

 65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35R25 Ill-posed problems for PDEs

Zbl 1185.65172
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### References:

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