Synopsis
Several Gradients.- Comparison of Two Gradients.- Continuous Steepest Descent in Hilbert Space: Linear Case.- Continuous Steepest Descent in Hilbert Space: Nonlinear Case.- Orthogonal Projections, Adjoints and Laplacians.- Introducing Boundary Conditions.- Newton's Method in the Context of Sobolev Gradients.- Finite Difference Setting: the Inner Product Case.- Sobolev Gradients for Weak Solutions: Function Space Case.- Sobolev Gradient in Non-inner Product Spaces: Introduction.- The Superconductivity Equations of Ginzburg-Landau.- Minimal Surfaces.- Flow Problems and Non-inner Product Sobolev Spaces.- Foliations as a Guide to Boundary Conditions.- Some Related Iterative Methods for Differential Equations.- A Related Analytic Iteration Method.- Steepest Descent for Conservation Equations.- A Sample Computer Code with Notes.- Bibliography.- Index.
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