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Taylor-Galerkin B-spline finite element method for the one-dimensional advection-diffusion equation. (English) Zbl 1197.65135

Summary: The advection-diffusion equation has a long history as a benchmark for numerical methods. Taylor-Galerkin methods are used together with the type of splines known as B-splines to construct the approximation functions over the finite elements for the solution of time-dependent advection-diffusion problems. If advection dominates over diffusion, the numerical solution is difficult especially if boundary layers are to be resolved. Known test problems are studied to demonstrate the accuracy of the method. Numerical results show the behavior of the method with emphasis on treatment of boundary conditions. Taylor-Galerkin methods are constructed by using both linear and quadratic B-spline shape functions. Results shown by the method are found to be in good agreement with the exact solution.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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