Publication

Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and the Stokes problems

Marco Picasso
2003
Journal Articles

Abstract

Stabilized finite elements on strongly anisotropic meshes are considered. The design of the stability coefficients is addressed for both the advection-diffusion and the Stokes problems when using continuous piecewise linear finite elements on triangles. Using the polar decomposition of the Jacobian of the a. ne mapping from the reference triangle to the current one, K, and from a priori error estimates, a new definition of the stability coefficients is proposed. Our analysis shows that these coefficients do not depend on the element diameter h(K) but on a characteristic length associated with K via the polar decomposition. A numerical assessment of the theoretical analysis is carried out.

Official source

https://infoscience.epfl.ch/entities/publication/92d0bb4f-ff60-4b37-90c1-fc2225fe7ce6

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Marco Picasso
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/92d0bb4f-ff60-4b37-90c1-fc2225fe7ce6

About this result

Related concepts (32)

Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.

Medial triangle

In Euclidean geometry, the medial triangle or midpoint triangle of a triangle △ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC, BC. It is the n = 3 case of the midpoint polygon of a polygon with n sides. The medial triangle is not the same thing as the median triangle, which is the triangle whose sides have the same lengths as the medians of △ABC. Each side of the medial triangle is called a midsegment (or midline). In general, a midsegment of a triangle is a line segment which joins the midpoints of two sides of the triangle.

Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.