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Recently there are several computational techniques have been successively implemented in dealing with non-smooth solutions for modeling of many physical phenomena such as fluid flows,semiconductor device simulation or in financial models etc.The mini-symposium will be concerned with in cases of where the solution contains deep gradients exhibiting the boundary layers or interior layers.For such problems,standard discretization methods such as a Galerkin finite element method or classical finite difference methods yield inaccurate oscillatory solutions.These layers are characterized by rapid transitions in the solution,and thus are very difficult to capture the solutions accurately without using a large number of unknowns or using fitted meshes in the layer regions.The aim of this minisymposium is to exchange ideas and explore novel techniques for resolving the boundary or interior layers while simulating the non-smooth model problems.