Poisson 2D FEM

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This example is a pure finite-element solve with no neural network component.

Problem Setup

The script assembles the weak form of a manufactured Poisson problem and solves the resulting linear system.

Step 1: Define the Weak Form

Instead of writing a pointwise PDE residual, the script builds bilinear and linear forms using FEM symbols.

Step 2: Assemble the Linear System

The weak form is transformed into a matrix system through jNO's FEM assembly workflow.

Step 3: Solve and Compare

The script computes the FEM solution and compares it to a known exact field.

What To Notice

• This chapter is about weak forms rather than PINN residuals.
• The assembly pipeline is useful as a reference even if your final method is neural.
• Pure FEM examples help validate the underlying PDE setup.

Download full script Back to 08 FEM and Variational PINNs

Script Snippet