A superconvergence result for solutions of compact operator equations
By R. Kulkarni. Bulletin of the Australian Mathematical Society, 2003
63 citations recorded by the source corpus.
Over the last 20 years, since the publication of Sloan's paper on the improvement by the iteration technique, various approaches have been proposed for post-processing the Galerkin solution of multi-dimensional second kind Fredholm Integral equation. These methods include the iterated Galerkin method proposed by Sloan, the Kantorovich method and the iterated Kantorovich method. Recently, Lin, Zhang and Yan have proposed interpolation as an alternative to the iteration technique. For an integral operator, with a smooth kernel using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree ≤ r − 1, previous authors have established an order r convergence for the Galerkin solution and 2r for the iterated Galerkin solution. Equivalent results have also been established for the interpolator projection at Gauss points and some interpolation post-processing technique. In this paper, a method is introduced and shown to have convergence of order 4r. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method.
Subfields: Atomic and Molecular Physics, and Optics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f0f85f4155adcb011c25d517b164ef81cf3349fc
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In Atomic and Molecular Physics, and Optics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- The Discrete Multi-Projection Method for Fredholm Integral Equations of the Second Kind (2007, methodology): “Recently [12] chose K n := K n +K n +K n to develop the algorithm for compact operator equations and obtain higher order super-convergence.”