Hi,
I want to do research in Finite element method, can anybody suggest me good problem (not yet solved)
Finite element method is used to approximate differential and integral equations to be able to apply numerical computations. There are many books on methodology. This one is in direct access http://www.sciencedirect.com/science/book/9780750678285 . Others with similar names you can find in library.
I can understand your question in 3 ways.
1) You want to extend numerical methodology. - Then try to find unsolved problem in such books. Convergence of numerical method to real solution is one of such problems. But usually such theorems are proved by mathematicians using abstract spaces and no computers.
2) You want to study numerical simulation for new applied problem or equation. - Usually such equations are derived by applied scientists who later apply numerical methods to them. Just find a collaborator who can derive new equation but knows little about numerical methods and needs your help.
3) It may also happen that method is known but requires too much memory or goes too slow. Then one can invent algorithms that save time or memory. Maybe this is what you want to do. Among applied problems you can find such in the physics of atmosphere and ocean. 3-dimensional problems require a lot of memory if the step is small. Still we have problems with accurate weather forecast. But then you have to look for partners among geophysicists. Physics of plasma is also numerically complicated.
Finite element method is used to approximate differential and integral equations to be able to apply numerical computations. There are many books on methodology. This one is in direct access http://www.sciencedirect.com/science/book/9780750678285 . Others with similar names you can find in library.
I can understand your question in 3 ways.
1) You want to extend numerical methodology. - Then try to find unsolved problem in such books. Convergence of numerical method to real solution is one of such problems. But usually such theorems are proved by mathematicians using abstract spaces and no computers.
2) You want to study numerical simulation for new applied problem or equation. - Usually such equations are derived by applied scientists who later apply numerical methods to them. Just find a collaborator who can derive new equation but knows little about numerical methods and needs your help.
3) It may also happen that method is known but requires too much memory or goes too slow. Then one can invent algorithms that save time or memory. Maybe this is what you want to do. Among applied problems you can find such in the physics of atmosphere and ocean. 3-dimensional problems require a lot of memory if the step is small. Still we have problems with accurate weather forecast. But then you have to look for partners among geophysicists. Physics of plasma is also numerically complicated.
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