A quadratic finite element is a type of finite element that uses quadratic polynomials to approximate the solution of partial differential equations, particularly in the context of spatially varying problems. This means that the shape functions used in the element formulation are quadratic, allowing for greater accuracy in representing curved geometries and capturing more complex behavior of solutions compared to linear elements. Quadratic finite elements are particularly useful when dealing with elliptic equations due to their ability to model variations in the solution more effectively.
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