Hello all, Could you help to guide on this problem for solving the Laplace equation with galerkin method,I am not sure how to proceed with this application in two dimension. Thanks in advance😇 Consider the Laplace equation V²u = 0, 0 0 u(x,0) = x(1-x), u(x,00) = 0, 0≤x≤1 Where the assumption is an approximation of the form, u(x, y)=c, (y)x(1-x). Create a differential equation for c, (y) by the Galerkin method along the x direction, and then solve it.

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Galerkin method

Thread starter FEM_DB
Start date Sep 11, 2021

Status: Not open for further replies.

Sep 11, 2021

FEM_DB

Student

Hello all,
Could you help to guide on this problem for solving the Laplace equation with galerkin method,I am not sure how to proceed with this application in two dimension.
Thanks in advance

Consider the Laplace equation
V²u = 0, 0<x< 1, u(0,y)=u(1,y)=0, 0<y<∞ for y>0 u(x,0) = x(1-x), u(x,00) = 0, 0≤x≤1
Where the assumption is an approximation of the form, u(x, y)=c,

x(1-x).
Create a differential equation for c,

by the Galerkin method along the x direction, and then solve it.