Galerkin Approximation

Galerkin approximation is a method used in mathematics and engineering to find approximate solutions to complex problems, especially those involving differential equations. It involves choosing a set of simpler, known functions (called basis functions) and expressing the solution as a combination of these. The method then adjusts the coefficients of these basis functions to best satisfy the original problem's conditions, effectively converting an complicated continuous problem into a manageable finite one. This approach is fundamental in numerical techniques like finite element analysis, enabling practical computations for problems that are otherwise analytically intractable.