A Newton-Krylov Algorithm for High-Order Finite Element Computation of Heat Conduction Problems

2012 ◽  
Author(s):  
Amir Nejat ◽  
Ehsan Mirzakhalili
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Discontinuous Galerkin ◽  
High Order ◽  
Coarse Mesh ◽  
Krylov Method ◽  
Cpu Time ◽  
Element Computation ◽  
Finite Element Computation

The solution of a high-order conduction problem with different orders of accuracy has been investigated in this paper. The high-order solutions are obtained using Discontinuous Galerkin (DG) finite element method. The problem is solved by implicit Newton-Krylov method for different accuracy orders. The convergence of the implicit technique is investigated in terms of the CPU time. The results show the possibility of achieving an accurate and smooth solution over a coarse mesh when the higher-order discretization is employed.

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.

A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems

2011 ◽  
Vol 9 (4) ◽  
pp. 1020-1039 ◽  
Author(s):  
Pedro Galán del Sastre ◽  
Rodolfo Bermejo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Second Order ◽  
High Order ◽  
Numerical Results ◽  
Convection Diffusion ◽  
Cpu Time ◽  
Better Than ◽  
Diffusion Problems

AbstractWe perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method. The numerical results show that for polynomials of degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes for the same number of degrees of freedom, however, for the same level of accuracy both methods are about the same in terms of CPU time. For polynomials of degree larger than 2, Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes in terms of both accuracy and CPU time; specially, for polynomials of degree 8 or larger. Also, we have performed tests on the parallelization of these schemes and the speedup obtained is quasi-optimal even with more than 100 processors.

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