Galerkin Method Fem. Standard approach to deriving a galerkin scheme is to multiply both sides of 1 by a test function v xn 0 integrate over the domain and seek a solution u x p ujφj x satisfying z ω v 2udv z ω vf dv v xn 0. The approach is usually credited to boris galerkin.
The galerkin fem for the solution of a differential equation consists of the following steps. In mathematics in the area of numerical analysis galerkin methods are a class of methods for converting a continuous operator problem to a discrete problem. In principle it is the equivalent of applying the method of variation of parameters to a function space by converting the equation to a weak formulation.
Standard approach to deriving a galerkin scheme is to multiply both sides of 1 by a test function v xn 0 integrate over the domain and seek a solution u x p ujφj x satisfying z ω v 2udv z ω vf dv v xn 0.
In mathematics in the area of numerical analysis galerkin methods are a class of methods for converting a continuous operator problem to a discrete problem. The approach is usually credited to boris galerkin. 1 multiply the differential equation by a weight function x and form the integral over the whole domain 2 if necessary integrate by parts to reduce the order of the highest order term x1x2 n1n2. Galerkin approximations 1 1 a simple example in this section we introduce the idea of galerkin approximations by consid ering a simple 1 d boundary value problem.
