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Abstract
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The existing local RBF methods use the strong form equation and approximate the solution in local subdomains instead of the whole domain. In the RBF-MLPG method, the unknown solution is approximated by RBFs in the whole domain and testing is done by constructing the weak-form equations over the local subdomains. This paper proposes to approximate the unknown solution locally in the RBF-MLPG method, i.e., in the localized RBF-MLPG method, both solution approximation and testing are treated locally. As a result, the final global matrix becomes sparser and more accurate solutions can be obtained. The method is applied for the numerical solution of elliptic PDEs. The comparison of the results demonstrates the effectiveness of the method.
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