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Overhauser elements in boundary element analysis. (English) Zbl 0726.65129
Authors’ summary: “The accuracy and the merit of the Overhauser cubic spline as an isoparametric representation in solving two-dimensional potential problems by the boundary element method is investigated. These functions are used to form a curvilinear boundary element which is intrinsically $$C^ 1$$-continuous between the elements. The resulting Overhauser element avoids the computational inefficiencies suffered by general cubic splines which require an additional variable to enforce derivative continuity between elements. Several numerical examples of phenomena governed by both the Poisson and biharmonic equations are presented and compared with existing numerical results or exact solutions.”
{Reviewer’s remark: The fundamental solution of the biharmonic equation is stated incorrectly in equation (6).}

##### MSC:
 65N38 Boundary element methods for boundary value problems involving PDEs 65D10 Numerical smoothing, curve fitting 65R20 Numerical methods for integral equations 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J40 Boundary value problems for higher-order elliptic equations 35C15 Integral representations of solutions to PDEs 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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