Discontinuous Galerkin approximations for Volterra integral equations of the first kind
IMA Journal of Numerical Analysis(2009)
摘要
Motivated by the problem of developing accurate and stable time-stepping methods for the single-layer potential equation for acoustic scattering from a surface, we present new convergence results for piecewise polynomial discontinuous Galerkin (DG) approximations of a first-kind Volterra integral equation of convolution kernel type, where the kernel K is smooth and satisfies K(0) ≠ 0. We show that...
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关键词
Volterra integral equations of the first kind,discontinuous Galerkin approximations,global convergence,local superconvergence
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