Semi-discrete Galerkin Approximations for the Single-Layer Equation on Lipschitz Curves
نویسنده
چکیده
We study a semi-discrete Galerkin method for solving the single-layer equation Vu = f with an approximating subspace of piecewise constant functions. Error bounds in Sobolev norms kkk s with ?1 s < 1 2 are proven and are of the same order as for the original Galerkin method. The distinctive features of the present work are that we handle irregular meshes and do not rely on Fourier methods. The main assumptions are that the quadrature rule used to approximate the inner product is a composite rule and that the underlying quadrature rule that is mapped to each subinterval has a suuciently small Peano constant.
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