Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations

2018 ◽  
Vol 56 (2) ◽  
pp. 732-765 ◽  
Author(s):  
Waixiang Cao ◽  
Chi-Wang Shu ◽  
Yang Yang ◽  
Zhimin Zhang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equations

scholarly journals Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

2015 ◽  
Vol 18 (1) ◽  
pp. 230-246 ◽  
Author(s):  
Seshu Tirupathi ◽  
Jan S. Hesthaven ◽  
Yan Liang
Keyword(s):  
Finite Element ◽  
Elliptic Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hyperbolic Equations ◽  
Applied Pressure ◽  
Magma Dynamics ◽  
Pressure Estimation ◽  
2D And 3D

AbstractDiscontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II. The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance at local chemical equilibrium and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equations and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the computational wall time without impacting the overall physical reliability in the modeling of important features of melt segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations.

Modeling Magma Dynamics with a Mixed Fourier Collocation — Discontinuous Galerkin Method

2011 ◽  
Vol 10 (2) ◽  
pp. 433-452 ◽  
Author(s):  
Alan R. Schiemenz ◽  
Marc A. Hesse ◽  
Jan S. Hesthaven
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hyperbolic Equations ◽  
Type System ◽  
High Order ◽  
Galerkin Methods ◽  
Magma Dynamics ◽  
Efficient Representation ◽  
Fourier Collocation

AbstractA high-order discretization consisting of a tensor product of the Fourier collocation and discontinuous Galerkin methods is presented for numerical modeling of magma dynamics. The physical model is an advection-reaction type system consisting of two hyperbolic equations and one elliptic equation. The high-order solution basis allows for accurate and efficient representation of compaction-dissolution waves that are predicted from linear theory. The discontinuous Galerkin method provides a robust and efficient solution to the eigenvalue problem formed by linear stability analysis of the physical system. New insights into the processes of melt generation and segregation, such as melt channel bifurcation, are revealed from two-dimensional time-dependent simulations.

Sign in / Sign up

Export Citation Format

Share Document