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A rational finite element basis /
A rational finite element basis.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1975.
|
| Colección: | Mathematics in science and engineering ;
v. 114. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges
- 2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities
- 4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols
- 6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION
- 9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX