The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential EquationsAbdul Kadir Aziz The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. |
Contents
Survey Lectures on the Mathematical | 1 |
Boundary Value Problems | 47 |
Theory of Approximation | 83 |
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adjoint analysis Applied approximate solution assume Babuška bilinear form boundary conditions boundary value problem bounded chapter coefficients compute consider constant cubic defined denote derivatives Dirichlet domain eigenvalue problem elliptic error estimates exists finite difference finite element method follows Galerkin methods given H₁ H₂ Hence Hilbert spaces independent of h inequality integral interpolation inverse assumption isoparametric Lemma linear M₁ M₂ mapping Math Mathematics matrix mesh nodal nodes norm numerical obtain operator parabolic partial differential equations patch test piecewise points polygon polynomial proof prove quadrature scheme rate of convergence satisfies smooth Sobolev spaces space H spline st,k subspaces t,k)-system theorem theory tion triangle tricubic unique variational principle vertex zero ди Эх