High Order Continuous Local-Conserving Fluxes and Finite-Volume-Like Finite Element Solutions for Elliptic Equations

2017 ◽  
Vol 55 (6) ◽  
pp. 2666-2686 ◽  
Author(s):  
Qingsong Zou ◽  
Li Guo ◽  
Quanling Deng
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Elliptic Equations ◽  
High Order ◽  
Order Continuous

Comparison of advection schemes for high-order h–p finite element and finite volume methods

2005 ◽  
Vol 10 (1-2) ◽  
pp. 233-252 ◽  
Author(s):  
M. Iskandarani ◽  
J.C. Levin ◽  
B.-J. Choi ◽  
D.B. Haidvogel
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
High Order ◽  
Advection Schemes

Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 100-104 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
High Order ◽  
Numerical Predictions ◽  
Volume Method ◽  
Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

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