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Publication# Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics

Abstract

Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column. DG methods for both advection and elliptic equations provide a robust and efficient solution to the problems of melt migration in the asthenospheric upper mantle. Assembling and solving the elliptic equation is the major bottleneck in these computations. To address this issue, adaptive mesh refinement and local timestepping methods have been proposed to significantly improve the computational wall time. The robustness of DG methods is demonstrated through two benchmark problems by modeling detailed structure of high-porosity dissolution channels and compaction-dissolution waves.

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Related concepts (28)

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Ontological neighbourhood

Jacobi elliptic functions

In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .

Asthenosphere

The asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is not well defined. The asthenosphere is almost solid, but a slight amount of melting (less than 0.1% of the rock) contributes to its mechanical weakness. More extensive decompression melting of the asthenosphere takes place where it wells upwards, and this is the most important source of magma on Earth.

Weierstrass elliptic function

In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

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