Publication

Function approximation on triangular grids: some numerical results using adaptive techniques

Luca Formaggia
2000
Journal Articles

Abstract

Applications of mesh adaptation techniques could be found in the numerical solution of PDE's or in the optimal triangulation of surfaces for shape representation or graphic display. The scope of this work is to verify through numerical experiments the effectiveness of some algorithms for the control of the L^2 error norm for piecewise linear approximation on 2D unstructured triangular meshes. The analysis could be extended to parametric surfaces and to the 3D case.

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Luca Formaggia
2000
Journal Articles

Abstract

Official source

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

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In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

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Function approximation on triangular grids: some numerical results using adaptive techniques

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