## [Libmesh-users] Role of exact solutions

 [Libmesh-users] Role of exact solutions From: John Pitney - 2005-07-15 00:12:40 Hi, I'm fairly new to finite element methods (my background is mostly in experimental physics), and I'm trying to learn the basics with libMesh and a copy of Bathe. In reading the examples, I see exact_solution prototypes declared, and sometimes actual exact values and exact derivatives are attached. What role does the exact_solution play in solving a real problem? What if one were solving the problem in Example 14, but didn't already know the the exact solution, u(r,\theta)? Sorry to bug the list with such a beginner question! If the answer is too complicated for an email response, a pointer to a good reference would be great. Thanks to all the developers for an impressive system! Best regards, John Pitney 

 [Libmesh-users] Role of exact solutions From: John Pitney - 2005-07-15 00:12:40 Hi, I'm fairly new to finite element methods (my background is mostly in experimental physics), and I'm trying to learn the basics with libMesh and a copy of Bathe. In reading the examples, I see exact_solution prototypes declared, and sometimes actual exact values and exact derivatives are attached. What role does the exact_solution play in solving a real problem? What if one were solving the problem in Example 14, but didn't already know the the exact solution, u(r,\theta)? Sorry to bug the list with such a beginner question! If the answer is too complicated for an email response, a pointer to a good reference would be great. Thanks to all the developers for an impressive system! Best regards, John Pitney 
 [Libmesh-users] Role of exact solutions From: John Peterson - 2005-07-15 03:41:53 Hi, Thanks for your interest in libMesh. In so-called "real" problems, the exact solution is rarely known so it plays no part. ex14 is a cooked-up example with an exact solution that contains a singularity in its first derivative. This is a classical problem to test convergence rates of adaptive finite element codes. The exact solution is only used to compute the error in the finite element solution in some appropriate norm (L2). -John John Pitney writes: > Hi, > > I'm fairly new to finite element methods (my background is > mostly in experimental physics), and I'm trying to learn > the basics with libMesh and a copy of Bathe. > > In reading the examples, I see exact_solution prototypes > declared, and sometimes actual exact values and exact > derivatives are attached. What role does the exact_solution > play in solving a real problem? What if one were solving > the problem in Example 14, but didn't already know the > the exact solution, u(r,\theta)? > > Sorry to bug the list with such a beginner question! If > the answer is too complicated for an email response, a > pointer to a good reference would be great. > > Thanks to all the developers for an impressive system! > > Best regards, > John Pitney