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Tikhonov regularization of an elliptic PDE

Author

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  • Sheela, S.
  • Singh, Arindama

Abstract

This paper considers an elliptic PDE with a small parameter multiplied with one of the derivatives. Recognizing the equation as an ill-posed equation, Tikhonov’s regularization is used to cast a related well-posed problem. A-priori estimates of the regularized solution and of the difference between the original and the regularized one are also derived. It is suggested that the regularized solution may be computed by using any well-known numerical method.

Suggested Citation

  • Sheela, S. & Singh, Arindama, 2001. "Tikhonov regularization of an elliptic PDE," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 1-4.
    • Handle: RePEc:eee:matcom:v:57:y:2001:i:1:p:1-4
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    Cited by:

    1. Rajan, M.P. & Reddy, G.D., 2015. "A variant of Tikhonov regularization for parabolic PDE with space derivative multiplied by a small parameter ∊," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 412-426.

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