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Finite Element Methods (G.1.8...)
Finite element applications: a practical guide to the FEM process
Okereke M., Keates S., Springer International Publishing, New York, NY, 2018. 472 pp. Type: Book (978-3-319671-24-6)
Much of modern engineering owes its existence to the finite element method (FEM), which makes the impossible possible while also allowing us to build bigger, safer, and cheaper than ever before. Yet, as with any other tool in the engineer’s ...
Feb 5 2019
Finite elements: theory and algorithms
Ganesan S., Tobiska L., Cambridge University Press, New York, NY, 2017. 216 pp. Type: Book (978-1-108415-70-5)
The finite-element method is a well-established mathematical tool that allows the use of computing techniques for the solution of problems arising in the sciences and engineering. As such, it is a topic that can be addressed from many different pe...
Feb 1 2018
A finite element method for high-contrast interface problems with error estimates independent of contrast
Guzmán J., Sánchez M., Sarkis M. Journal of Scientific Computing 73(1): 330-365, 2017. Type: Article
Guzmán et al. explain their method with a polygonal, convex, tubular domain, and an immersed interface definable with a function with the first derivative, which does not change in time. The jumps across a discontinuity are defined as expressions ...
Jan 24 2018
An adaptive finite element method for the wave scattering with transparent boundary condition
Jiang X., Li P., Lv J., Zheng W. Journal of Scientific Computing 72(3): 936-956, 2017. Type: Article
Jiang et al. discuss the numerical solution of acoustic wave scattering by an obstacle in two dimensions. The problem is defined on an open domain and requires a truncation of the domain (see Givoli ) using one of the following well-known metho...
Dec 14 2017
Finite difference/finite element methods for distributed-order time fractional diffusion equations
Bu W., Xiao A., Zeng W. Journal of Scientific Computing 72(1): 422-441, 2017. Type: Article
Bu et al. discretize the fractional diffusion equation in time using a modified compound trapezoid formula, and the Caputo fractional derivative in space is done using the L1 method, thus obtaining an unconditionally stable semi-discrete variation...
Aug 9 2017
Advanced finite element simulation with MSC Marc: application of user subroutines
Javanbakht Z., Öchsner A., Springer International Publishing, New York, NY, 2017. 347 pp. Type: Book (978-3-319476-67-4)
Commercial (and other) finite element packages give their users the option to replace some of the package’s built-in subroutines with user-defined customized versions. This feature provides great flexibility and permits, for example, enhanci...
Jul 13 2017
A weak Galerkin finite element method for a type of fourth order problem arising from fluorescence tomography
Wang C., Zhou H. Journal of Scientific Computing 71(3): 897-918, 2017. Type: Article
The finite element method (FEM) was introduced by engineers  for the solution of partial differential equations (PDEs) and analyzed later, for example, by Ciarlet ....
Jul 3 2017
Finite element methods for computational fluid dynamics: a practical guide
Kuzmin D., Hämäläinen J., SIAM, Philadelphia, PA, 2014. 321 pp. Type: Book (978-1-611973-60-0)
Kuzmin and Hämäläinen’s book provides a general overview of finite element methods (FEMs) when applied to computational fluid dynamics (CFD), giving a gentle introduction to these fields, a survey of recent advanced works in t...
Aug 28 2015
The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Zhang B., Liu H., Chen F., Wang J. Journal of Computational Physics 263151-176, 2014. Type: Article
Zhang et al. propose a new fractional-step method for the numerical solution of advection equations with stiff source terms. In general, it is too difficult to obtain satisfactory numerical approximate solutions for stiff reaction problems, becaus...
Oct 29 2014
Numerical integration on GPUs for higher order finite elements
Banaś K., P
aszewski P., Macio
P. Computers & Mathematics with Applications 67(6): 1319-1344, 2014. Type: Article
Finite element methods (FEMs) are numerical methods for finding approximate solutions to partial differential equations. When a problem is presented, a mesh and a finite element space are required to be defined. Regular choices for meshes are tetr...
Oct 22 2014
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