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We study Tikhonov regularization for solving ill--posed operator equationswhere the solutions are functions defined on surfaces. One contribution of thispaper is an error analysis of Tikhonov regularization which takes into accountperturbations of the surfaces, in particular when the surfaces are approximatedby spline surfaces. Another contribution is that we highlight the analysis ofregularization for functions with range in vector bundles over surfaces. Wealso present some practical applications, such as an inverse problem ofgravimetry and an imaging problem for denoising vector fields on surfaces, andshow the numerical verification.

Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces