Numerical solution of differential and integral equations
In this work we consider finite superelement method for the velocity skin-layer problem, which arises from mathematical modelling of processes in electro-magnetic launchers. We consider this problem in two spatial dimensions. In this case, from the mathematical point of view, it leads to the nonstationary convection-diffusion problem in the domain with complex geometry.
We introduce the variational equation which natural Petrov-Galerkin approximation leads to Fedorenko Finite Superelemet Method (FSEM). FSEM is considered as Petrov-Galerkin approximation of the certain problem for traces of boundary-value problem solution at the boundaries of superelements. To constract variational equation mentioned above Poincare-Steklov operators were used.
We also consider regularized FSEM scheme. To construct it we use nonlinear artificial diffusion.
Some results on combined finite superelements/finite elements approximations are presented. Some numerical results are presented.
Note. Abstracts are published in author's edition
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