represents a Laplacian term with model variables vars.


  • The Laplacian term is a differential operator term used to describe many physical phenomena, such as potentials, heat transfer, acoustics, structural mechanics and fluid dynamics.
  • LaplacianPDETerm returns a differential operators term to be used as a part of partial differential equations:
  • LaplacianPDETerm can be used to model Laplacian equations with dependent variable , independent variables and time variable .
  • Stationary model variables vars are vars={u[x1,,xn],{x1,,xn}}.
  • Time-dependent model variables vars are vars={u[t,x1,,xn],{x1,,xn}} or vars={u[t,x1,,xn],t,{x1,,xn}}.
  • The Laplacian is realized as a DiffusionPDETerm with 1 as a diffusion coefficient resulting in .
  • The diffusion coefficient 1 affects the meaning of NeumannValue.


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Basic Examples  (2)

Define a stationary Laplacian term:

Find eigenvalues of a Laplacian term:

Scope  (2)

Set up a time-dependent Laplacian:

Find eigenvalues and vectors of a Laplacian term in a 3D shell:

Visualize the result:

Wolfram Research (2020), LaplacianPDETerm, Wolfram Language function,


Wolfram Research (2020), LaplacianPDETerm, Wolfram Language function,


Wolfram Language. 2020. "LaplacianPDETerm." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2020). LaplacianPDETerm. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2022_laplacianpdeterm, author="Wolfram Research", title="{LaplacianPDETerm}", year="2020", howpublished="\url{}", note=[Accessed: 29-November-2022 ]}


@online{reference.wolfram_2022_laplacianpdeterm, organization={Wolfram Research}, title={LaplacianPDETerm}, year={2020}, url={}, note=[Accessed: 29-November-2022 ]}