Two-scale composite finite element method for parabolic problems in convex and nonconvex polygonal domains

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The main objective of this thesis is to study a priori error analysis of the two-scale com- posite finite element (CFE) method for parabolic initial-boundary value problems (IBVPs) in two-dimensional convex and nonconvex polygonal domains. When the physical domain is non- convex or very complicated, the standard finite element method (FEM) requires to generate finite element mesh that resolves the domain boundary. As a result, the degrees of freedom of such finite element space are distributed in a nonoptimal way with respect to the approxi- mation quality which drastically increases the minimal dimension of the finite element space. Whereas, the CFE discretizations are based on the two-scale grid refinement: In the interior of the domain at a proper distance from the boundary, the solution is approximated by a coarse-scale parameter H whereas the near-boundary triangles are discretized by a fine-scale parameter h which approximates the Dirichlet boundary conditions.
Supervisor: Rajen Kumar Sinha