Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared
Advection breaks the symmetry of the stiffness matrix, and the minimum total potential energy principle goes with it. Here is the real cause of Galerkin oscillations and what stabilization buys instead.
One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis
The minimum number of Gauss points in a DG cell integral is set by the degree of the integrand, not by the mesh. Going from three points to two changes nothing; going to one destroys the scheme.
Skew the Element 45° and the Stiffness Grows 2.5x — Metric Tensors and Constitutive Tensor Transformation
In curvilinear coordinates, writing strain as covariant components means the constitutive tensor has to move too. Skip that step and every skewed element reports the wrong stiffness.
Thinner Means Stiffer — Shear Locking in Shell Elements and the MITC Tying Fix
A linear shell element gets stiffer, not weaker, as it thins out. The cause is one line: shear strain obtained by differentiating displacements.
Why Does the Bridge Sag Like That? The Direct Stiffness Method for Trusses
Assembling bar element stiffness matrices to solve truss displacements with FEM
Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis
Step-by-step summary from DGM weak form derivation to Gauss quadrature and unstructured grid implementation.
FEM for Rigid Body Dynamics: Quaternion-based Rotation Handling and Inertia Tensors
Methods for representing rotations with quaternions and handling inertia tensors in FEM rigid body simulations.
FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques
A comparison of the mathematical origins, pros and cons, and best application areas for the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM).