Volume 1, Issue 2 (12-2020)
MACO 2020, 1(2): 35-43 |
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Abstract: (1644 Views)
In this paper, we develop a numerical method to solve a famous free boundary PDE called the one dimensional Stefan problem.
First, we rewrite the PDE as a variational inequality problem (VIP). Using the linear finite element method, we discretize the variational inequality and achieve a linear complementarity problem (LCP). We present some existence and uniqueness theorems for solutions of the variational inequalities and free boundary problems. Finally we solve the LCP numerically by applying a modification of the active set strategy.
First, we rewrite the PDE as a variational inequality problem (VIP). Using the linear finite element method, we discretize the variational inequality and achieve a linear complementarity problem (LCP). We present some existence and uniqueness theorems for solutions of the variational inequalities and free boundary problems. Finally we solve the LCP numerically by applying a modification of the active set strategy.
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