Groundwater and surface water interaction is a common process of the hydrologic cycle but still challenging to be addressed in a general context. A special case of groundwater-surface water interaction is the seepage from a river/stream or canal into an adjacent phreatic aquifer, where the groundwater flow in the vicinity of the stream is crucial while the aquifer is supposed to extend to infinity, especially for the mathematical analysis. Herein, numerical solutions of 1-D Boussinesq equation and 2-D Richards equation are presented by embedding infinite elements in the finite element analysis to discretise only the key subsurface flow region close to the stream. By using the infinite elements, which extend to infinity to one direction according to appropriate shape functions, the total number of elements required to discretise the simulation area is substantially reduced. As a result, computationally efficient solutions are obtained, which is particularly important for the two-dimensional saturated-unsaturated groundwater flow described by the Richards equation, as well as sufficiently accurate, both in terms of groundwater recharge and water table in the vicinity of the stream. The finite-infinite element approach could be useful to derive accurate and fast numerical solutions under the investigation of several scenarios.

地下水和地表水的相互作用是水文循环的一个常见过程，但在一般情况下仍然具有挑战性。地下水-地表水相互作用的一个特例是从河流/溪流或运河渗入相邻的潜水含水层，其中溪流附近的地下水流动至关重要，而含水层应该延伸到无限远，特别是对于数学分析。在此，一维 Boussinesq 方程和二维理查兹方程的数值解通过在有限元分析中嵌入无限元以仅离散靠近河流的关键地下流动区域来呈现。通过使用无限元，根据适当的形状函数向一个方向扩展到无限，离散模拟区域所需的元素总数大大减少。结果，获得了计算效率高的解，这对于 Richards 方程描述的二维饱和-非饱和地下水流尤其重要，并且在地下水补给和地下水位附近的地下水位方面都足够准确。溪流。有限无限元方法可用于在对几种情况的调查下获得准确和快速的数值解。在地下水补给和河流附近的地下水位方面。有限无限元方法可用于在对几种情况的调查下获得准确和快速的数值解。在地下水补给和河流附近的地下水位方面。有限无限元方法可用于在对几种情况的调查下获得准确和快速的数值解。