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Free boundary problem

About: Free boundary problem is a(n) research topic. Over the lifetime, 15390 publication(s) have been published within this topic receiving 274687 citation(s).

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01 Apr 1985
Abstract: Foreword Preface 1. Sobolev spaces 2. Regular second-order elliptic boundary value problems 3. Second-order elliptic boundary value problems in convex domains 4. Second-order boundary value problems in polygons 5. More singular solutions 6. Results in spaces of Holder functions 7. A model fourth-order problem 8. Miscellaneous Bibliography Index.

4,904 citations

Journal ArticleDOI
Abstract: The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining \"°°-order\" approximations and low n, even when singularities are present. General theoretical analysis of the numerical process. Numerical experiments with linear and nonlinear, elliptic and mixed-type (transonic flow) problemsconfirm theoretical predictions. Similar techniques for initial-value problems are briefly

2,923 citations

01 Jan 1987
Abstract: Part 1 Hypergeometric Functions and Elliptic Integrals: Some Basic Topics In Analytical Dynamics The Problem of Two Bodies Two-Body Orbits and the Initial-Value Problem Solving Kepler's Equation Two-Body Orbital Boundary Value Problem Solving Lambert's Problem Appendices Part 2 Non-Keplerian Motion: Patched-Conic Orbits and Perturbation Methods Variation of Parameters Two-Body Orbital Transfer Numerical Integration of Differential Equations The Celestial Position Fix Space Navigation Appendices

1,997 citations

01 Jan 1984
Abstract: 1. Moving boundary problems: formulation 2. Free boundary problems: formulation 3. Analytical solutions 4. Front-tracking methods 5. Front-fixing methods 6. Fixed-domain methods 7. Analytical solution of seepage problems 8. Numerical solution of free boundary problems References Author index Subject index

1,880 citations

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