近年來，由於全球氣溫上升，兩極的冰川開始被大家重視。與其相關的
科學領域是冰層動力學，一門探討冰層受到外力後如何運動的自然科學。
在數學領域上，冰層模型多用非線性斯托克斯方程描述。我們使用弱伽遼
金有限元素法求解此偏微分方程，並且利用相同方法下解線性托克斯方程
的結果及固定點疊代法，給出有效的估計結果。

Recently, due to global temperature raise, the polar glaciers are gradually emphasized.
The related science field is glacier dynamics, describe how glaciers move
under the environmental force. The glacier model is usually modelled by nonlinear
Stokes equation in mathematics. We use weak Galerkin finite element method
to solve this PDE and give an effective approximation by the fixed point iteration
method and the result of solving the linear Stokes equation in the weak Galerkin
finite element method.

Acknowledgements
摘要i
Abstract ii
1 Introduction 1
1.1 Motivation 1
1.2 The model of glaciers 2
1.3 The Stokes equation 3
2 Method and schemes 7
2.1 Finite element space 7
2.2 Implementation of the method 10
2.3 Error estimate 11
3 Numerical Experiences 15
3.1 Linear case Result: variable coefficient 15
3.2 Nonlinear case Result: Main case 18
4 Conclusion and Future works 23
References 25

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