Abstract
The rate of convergence for numerical methods approximating differential equations are often drastically reduced from lack of regularity in the solution. Typical examples are problems with singular source terms or discontinuous material coefficients. We shall discuss the technique of local regularization for handling these problems. New numerical methods are presented and analyzed and numerical examples are given. Some serious deficiencies in existing regularization methods are also pointed out.
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Tornberg, AK., Engquist, B. Regularization Techniques for Numerical Approximation of PDEs with Singularities. Journal of Scientific Computing 19, 527–552 (2003). https://doi.org/10.1023/A:1025332815267
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DOI: https://doi.org/10.1023/A:1025332815267