Finite elements : theory, fast solvers, and applications in solid mechanics / Dietrich Braess ; translated by Larry L. Shumaker.

By: Braess, Dietrich, 1938-Material type: TextTextLanguage: English Publication details: Cambridge ; New York : Cambridge University Press, 2001Edition: 2nd edDescription: xvii, 352 p. : ill. ; 23 cmISBN: 0521011957 (pbk.); 9780521011952 (pbk.)Uniform titles: Finite Elemente. English Subject(s): Finite element method | Elasticity -- Mathematical modelsDDC classification: 620.00151535 LOC classification: TA347.F5 | B7313 2001
Contents:
Examples and Classification of PDE's -- Classification of PDE's -- Well-posed problems -- The Maximum Principle -- Corollaries -- Finite Difference Methods -- Discretization -- Discrete maximum principle -- A Convergence Theory for Difference Methods -- Consistency -- Local and global error -- Limits of the convergence theory -- Conforming Finite Elements -- Sobolev Spaces -- Introduction to Sobolev spaces -- Friedrichs' inequality -- Possible singularities of H[superscript 1] functions -- Compact imbeddings -- Variational Formulation of Elliptic Boundary-Value Problems of Second Order -- Variational formulation -- Reduction to homogeneous boundary conditions -- Existence of solutions -- Inhomogeneous boundary conditions -- The Neumann Boundary-Value Problem. A Trace Theorem -- Ellipticity in H[superscript 1] -- Boundary-value problems with natural boundary conditions -- Neumann boundary conditions -- Mixed boundary conditions -- Proof of the trace theorem -- Practical consequences of the trace theorem -- The Ritz-Galerkin Method and Some Finite Elements -- Model problem -- Some Standard Finite Elements -- Requirements on the meshes -- Significance of the differentiability properties -- Triangular elements with complete polynomials -- Remarks on C[superscript 1] elements -- Bilinear elements -- Quadratic rectangular elements -- Affine families -- Choice of an element -- Approximation Properties -- The Bramble-Hilbert lemma -- Triangular elements with complete polynomials -- Bilinear .quadrilateral elements -- Inverse estimates
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Books Books School of Engineering and Technology
School of Engineering and Technology
620.00151535 BDF (Browse shelf (Opens below)) Available 2386
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.Includes index

.Includes bibliographical references (p. 337-347)

Examples and Classification of PDE's -- Classification of PDE's -- Well-posed problems -- The Maximum Principle -- Corollaries -- Finite Difference Methods -- Discretization -- Discrete maximum principle -- A Convergence Theory for Difference Methods -- Consistency -- Local and global error -- Limits of the convergence theory -- Conforming Finite Elements -- Sobolev Spaces -- Introduction to Sobolev spaces -- Friedrichs' inequality -- Possible singularities of H[superscript 1] functions -- Compact imbeddings -- Variational Formulation of Elliptic Boundary-Value Problems of Second Order -- Variational formulation -- Reduction to homogeneous boundary conditions -- Existence of solutions -- Inhomogeneous boundary conditions -- The Neumann Boundary-Value Problem. A Trace Theorem -- Ellipticity in H[superscript 1] -- Boundary-value problems with natural boundary conditions -- Neumann boundary conditions -- Mixed boundary conditions -- Proof of the trace theorem -- Practical consequences of the trace theorem -- The Ritz-Galerkin Method and Some Finite Elements -- Model problem -- Some Standard Finite Elements -- Requirements on the meshes -- Significance of the differentiability properties -- Triangular elements with complete polynomials -- Remarks on C[superscript 1] elements -- Bilinear elements -- Quadratic rectangular elements -- Affine families -- Choice of an element -- Approximation Properties -- The Bramble-Hilbert lemma -- Triangular elements with complete polynomials -- Bilinear
.quadrilateral elements -- Inverse estimates

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