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The convection–diffusion equation

A. M. Stuart and E. Söli.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 22847 words.

This chapter concerns the statement of the steady convection–diffusion equation and its weak formulation. This is followed by a description of finite element discretization and properties...

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Finite Elements and Fast Iterative Solvers

Howard Elman, David Silvester and Andy Wathen.

June 2014; p ublished online September 2014 .

Book. Subjects: Mathematics; Optimisation. 496 pages.

The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part (Chapters 1 through 5) covers...

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Models of Incompressible Fluid Flow

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 3747 words.

This preliminary chapter gives a brief introduction to the equations studied in depth in the book, as they are used to model incompressible fluids.

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The Navier–Stokes Equations

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 14039 words.

This chapter concerns the statement and properties of the steady Navier–Stokes equations and the corresponding weak formulation. This includes discussion of stability theory, bifurcation...

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Optimization with PDE Constraints

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 7064 words.

This chapter is an introduction to techniques of optimization with constraints defined by partial differential equations. It discusses optimization and discretization methods together with...

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The Poisson Equation

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 28536 words.

This chapter concerns the statement of the Poisson equation and its weak formulation. This is followed by a description of finite element discretization and properties of the discrete...

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Solution of discrete convection–diffusion problems

A. M. Stuart and E. Söli.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 22013 words.

This chapter concerns iterative methods for solution of discrete convection–diffusion equations. It discusses Krylov subspace methods, principally the generalized minimum residual method,...

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Solution of Discrete Navier–Stokes Problems

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 25973 words.

This chapter concerns iterative methods for solution of the discrete Navier–Stokes equations. The emphasis is on preconditioning methods tailored to the structure of the linearized...

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Solution of discrete Poisson problems

A. M. Stuart and E. Söli.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 23860 words.

This chapter concerns iterative methods for solution of discrete convection-diffusion equations. It discusses Krylov subspace methods, principally the generalized minimum residual method,...

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Solution of Discrete Stokes Problems

Howard C. Elman, David J. Silvester and Andrew J. Wathen.

in Finite Elements and Fast Iterative Solvers

June 2014; p ublished online September 2014 .

Chapter. Subjects: Mathematics; Optimisation. 13840 words.

This chapter concerns iterative methods for solution of the discrete Stokes equations. It discusses the preconditioned minimum residual method, preconditioning strategies and multigrid...

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