A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method

Abstract

This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.

ERUPTING FILAMENTS WITH LARGE ENCLOSING FLUX TUBES AS SOURCES OF HIGH-MASS THREE-PART CMEs, AND ERUPTING FILAMENTS IN THE ABSENCE OF ENCLOSING FLUX TUBES AS SOURCES OF LOW-MASS UNSTRUCTURED CMEs

“…Yu et al (2014) show such jet CMEs propagating to large distances from the Sun and into interplanetary space. A recent study of a rapid series of 12 jet CMEs arising from a single region over a ∼2-day period was made by Alzate & Morgan (2015), giving mass estimates in the range of 0.4-3.2×10 14 g, with a mean mass of 1.8×10 14 g. These are considerably less massive than even the category 4 events. The category 4 events lack a clear 3-part structure, but they do contain internal structure, albeit complicated and difficult to interpret.…”

“…The category 4 events lack a clear 3-part structure, but they do contain internal structure, albeit complicated and difficult to interpret. The jet CMEs presented by Alzate & Morgan (2015) lack internal structure, they appear as unstructured 'puffs' of material.…”

Numerical solution of the Laplace equation: electrostatic potential

“…The numerical solution is based on the finite difference method [6,7]. In the two-dimensional case we treat the plate as a mesh of discrete points.…”

“…The simplest case is that where the electric potential at the border is a fixed value, this type of condition is known as a Dirichlet boundary condition. Another type of condition is the Neumann boundary condition, which has as its data the derivative at the border [6,7].…”