Hi Alex,
The "pdeInterpolant" function in MATLAB is used to interpolate solutions of partial differential equations (PDEs) at arbitrary points within the geometry. However, the specific numerical method used for interpolation in pdeInterpolant is not explicitly documented in the MATLAB documentation.
From general principles of finite element methods (FEM) and interpolation, we can infer some details:
- Continuity: For 2D quadratic triangulations, you can typically expect "C0 continuity". This means the interpolant is continuous, but its first derivative may not be continuous across element boundaries. While "C1 continuity" requires both the function and its first derivative to be continuous across element boundaries. Achieving "C1 continuity" typically involves using more complex elements or additional constraints, which is uncommon for standard quadratic elements in finite element methods.
- Interpolation Method: The interpolation is likely based on shape functions used in "FEM". For quadratic elements, these shape functions is usually done using second-degree polynomials, which provide a higher degree of accuracy compared to linear elements.
You may refer to the below MathWorks documentation links if you need more precise control over the interpolation method or continuity:
