mass lumped finite element scheme

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biblionaut
Posts: 4
Joined: Tue May 28, 2019 3:03 pm
Location: Germany

mass lumped finite element scheme

Post by biblionaut » Tue Jun 16, 2020 9:01 am

Hello,

I'm currently writing my master thesis. I used Hydrus-1D for it. Its a great program and very flexible. Im now writing on the theoretical background of the program. In "The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media" by Šimůnek, Jirka et al. 2008 the scheme used to produce the finite elements along the one dimensional soil profil is described as "mass-lumped linear finite elements scheme" (p. 105).
I'm not all too familiar with finite elements in general but i know what they are, how they work, why they are used as well as the basic types. But i have never heard of this scheme in particular. i also cant find literature online which would explain what this scheme does, at least not one that is more accessable than only giving the equations.
I would be very thankful if someone could give me a basic explaination of how the "mass-lumped linear finite elements scheme" works or give me a source that explains it.

Sincerely

Jonas

Jirka
Posts: 4961
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

Re: mass lumped finite element scheme

Post by Jirka » Tue Jun 16, 2020 5:42 pm

I suggest the following two publications. The first one you can download from https://www.pc-progress.com/en/Default. ... -genuchten:

van Genuchten, M.Th., Numerical solutions of the one dimensional saturated unsaturated flow equation. Research Report No. 78 WR 9, Water Resources Program, Dept. of Civil Engineering, Princeton Univ., Princeton, NJ, 91 p., 1978.

Neuman, S. P., Finite element computer programs for flow in saturated-unsaturated porous media, Second Annual Report, Project No. A10-SWC-77, Hydraulic Engineering Lab., Technion, Haifa, Israel, 1972.

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