本論文首先簡要介紹冰層動力學中的淺冰近似方程。為了避免在冰層邊緣處梯度產生奇異性，可透過變數變換將其轉換為 $p$-Laplace 方程。本研究採用不連續有限元素法求解此方程。考慮到方程的退化特性，我們於數值計算中引入正則化參數 $delta$ 以避免由此性質引發的問題。此外，為加速疊代過程，我們在固定點迭代中引入Anderson加速方法，並使用阻尼參數以減緩固定點算子非收縮性所帶來的影響。最後，我們使用 FEniCS 函式庫並在 Google Colaboratory 平台上實作數值結果。

This thesis begins with a brief introduction to the shallow ice approximation (SIA) equation in ice sheet dynamics. To avoid singularities in the gradient near the ice margin, the SIA can be transformed into a $p$-Laplace equation through a change of variables. This study use the discontinuous Galerkin (DG) method to solve the equation. Considering the degenerate nature of the equation, a regularization parameter $delta$ is introduced in the numerical computation to avoid this issue. In addition, to accelerate the iterative process, we apply Anderson acceleration (AA) to the fixed-point iteration and introduce a damping parameter to reduce the effects caused by the non-contractive nature of the fixed-point operator. Finally, we implement numerical results using the FEniCS library on the Google Colaboratory platform.

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