Die Infinite Element Methode wird hauptsächlich bei der Berechung singulärer Lösungen partieller Differentialgleichungen und bei deren Lösung von Gleichungen auf unbeschränkten Gebieten angewandt. In diesem Buch wird ein spezielles numerisches Verfahren vorgestellt, das bisher noch relativ unbekannt geblieben ist.
Die Infinite Element Methode wird hauptsächlich bei der Berechung singulärer Lösungen partieller Differentialgleichungen und bei deren Lösung von Gleichungen auf unbeschränkten Gebieten angewandt. In diesem Buch wird ein spezielles numerisches Verfahren vorgestellt, das bisher noch relativ unbekannt geblieben ist.
Due December 1994. Summary of contents: Chapter I: Two dimensional exterior problems of the Laplace equation; Fourier methods; Iterative methods; General elements; Three dimensional exterior problems of the Laplace equation; Problems on other unbounded domains; Corner problems; Nonhomogeneous boundary conditions; Plane elasticity problems; Calculation of stress intensity factors; Exterior Stokes problems; Non-similar problems Chapter II: Foundations of Algorithm; Infinite element spaces; Shift matrices; Furhter discussion for the infinite element spaces and the shift matrices; Shift matrices for the plane elasticity problems; Combined stiffness matrices; Iterative method of the first type; Iterative method of the second type; General elliptic systems; Exterior Stokes problems; Nonhomogeneous equations and the Helmholtz equation; Chapter III: SSome auxiliary inequalities; Approximate properties of piecewise polynomials - H1 and L2 convergence; Maximum principle and uniform convergence; A superconvergence estimate; Term by term convergence near the corner Chapter IV Boundary value problems and Eigenvalue problems; Stress intensity factors; Stokes external flow; Navier Stokes external flow
Due December 1994. Summary of contents: Chapter I: Two dimensional exterior problems of the Laplace equation; Fourier methods; Iterative methods; General elements; Three dimensional exterior problems of the Laplace equation; Problems on other unbounded domains; Corner problems; Nonhomogeneous boundary conditions; Plane elasticity problems; Calculation of stress intensity factors; Exterior Stokes problems; Non-similar problems Chapter II: Foundations of Algorithm; Infinite element spaces; Shift matrices; Furhter discussion for the infinite element spaces and the shift matrices; Shift matrices for the plane elasticity problems; Combined stiffness matrices; Iterative method of the first type; Iterative method of the second type; General elliptic systems; Exterior Stokes problems; Nonhomogeneous equations and the Helmholtz equation; Chapter III: SSome auxiliary inequalities; Approximate properties of piecewise polynomials - H1 and L2 convergence; Maximum principle and uniform convergence; A superconvergence estimate; Term by term convergence near the corner Chapter IV Boundary value problems and Eigenvalue problems; Stress intensity factors; Stokes external flow; Navier Stokes external flow
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