This numerical model has a solution procedure that exploits approximations to the connectivity of the elements and to the continuity of stress and displacements between the elements.

This numerical model has a solution procedure that exploits approximations to the connectivity of the elements and to the continuity of stress and displacements between the elements.

• A. Finite Difference Method
• B. Boundary Element Method
• C. Finite Element Method
• D. Spectral Method

Answer: (C)

The idea being tested is how a numerical method builds a solution by dividing the domain into small, connected pieces and enforcing continuity across their interfaces. This is exactly how the finite element method works. It partitions the domain into elements that meet at shared nodes, then represents the unknown field (like displacement) inside each element with simple functions. The values at the shared nodes are the unknowns, so neighboring elements are tied together through these nodes. When you assemble all the local element equations into a global system, you’re using that connectivity to ensure the field is continuous across element boundaries and that forces and stresses balance at every interface. Once you solve for the nodal values, you can recover strains and stresses inside each element consistently from the same connectivity and shape functions. In contrast, finite difference methods discretize equations on a grid and don’t rely on an explicit network of interconnected elements; boundary element methods focus primarily on discretizing boundaries rather than the interior, and spectral methods use global basis functions over the whole domain rather than subdividing it into connected elements. Those approaches don’t exploit element connectivity in the same way as the finite element method, which is why this description points to the finite element approach.

The idea being tested is how a numerical method builds a solution by dividing the domain into small, connected pieces and enforcing continuity across their interfaces. This is exactly how the finite element method works. It partitions the domain into elements that meet at shared nodes, then represents the unknown field (like displacement) inside each element with simple functions. The values at the shared nodes are the unknowns, so neighboring elements are tied together through these nodes. When you assemble all the local element equations into a global system, you’re using that connectivity to ensure the field is continuous across element boundaries and that forces and stresses balance at every interface. Once you solve for the nodal values, you can recover strains and stresses inside each element consistently from the same connectivity and shape functions.

In contrast, finite difference methods discretize equations on a grid and don’t rely on an explicit network of interconnected elements; boundary element methods focus primarily on discretizing boundaries rather than the interior, and spectral methods use global basis functions over the whole domain rather than subdividing it into connected elements. Those approaches don’t exploit element connectivity in the same way as the finite element method, which is why this description points to the finite element approach.