在這篇論文中, 我們以高階不連續有限元素法解橢圓界面問題。在數值方法中, 使用Guyomarc’h, Lee 與Jeon 所提出的數值通量, 與其不同是, 我們使用曲邊四邊形元素取代三角形元素, 而在函數基底方面, 使用Q^k-polynomials 取代P^k-polynomials。
在數值實驗中, 當基底函數之維度設定為k 階, 則得以驗證數值解之誤差收斂速度為k + 1 階, 而在實際應用上, 可任意設定基底函數之維度, 以得到所需要之誤差收斂速度。

In this paper, we deal with a high-order accurate discontinuous Galerkin method for the numerical solution of the elliptic interface problem with discontinuous media property and jumps on interface. In this work, we use the local discontinuous Galerkin (LDG) methods with the numerical flux proposed by Guyomarc’h, Lee, and Jeon, and instead of the triangular elements and the P^k-polynomials basis functions, we use the quadrilateral elements and the Q^k-polynomials basis functions.
The numerical experiments show that the numerical solution converges with order k+1 when all the local spaces contain the polynomials of degree k.

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