scholarly journals High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces

2017 ◽  
Vol 111 ◽  
pp. 64-91 ◽  
Author(s):  
Jason Albright ◽  
Yekaterina Epshteyn ◽  
Michael Medvinsky ◽  
Qing Xia
Keyword(s):  
Elliptic Problems ◽  
High Order ◽  
Numerical Schemes ◽  
Material Interfaces ◽  
Difference Potentials

A high-order solver for aerodynamic flow simulations and comparison of different numerical schemes

2017 ◽  
Author(s):  
Sergey Mikhaylov ◽  
Alexander Morozov ◽  
Vladimir Podaruev ◽  
Alexey Troshin
Keyword(s):  
High Order ◽  
Numerical Schemes ◽  
Flow Simulations

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

scholarly journals High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 200 ◽  
Author(s):  
He Yang
Keyword(s):  
Numerical Methods ◽  
Gordon Equation ◽  
Free Particle ◽  
High Order ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Optimal Error Estimates ◽  
Numerical Schemes ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

Efficiency of high order numerical schemes for momentum advection

2007 ◽  
Vol 67 (1-2) ◽  
pp. 31-46 ◽  
Author(s):  
Nina G. Winther ◽  
Yves G. Morel ◽  
Geir Evensen
Keyword(s):  
High Order ◽  
Numerical Schemes
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