An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid

•Boundary conditions on the hydrogel surface are naturally embedded in the weak form.•With proper test functions, the weak form recovers the dissipative energy law.•The displacement extension algorithm captures interfacial displacement accurately.•The ALE method tracks the moving interface as well as the deforming solid skeleton.•The numerical results show excellent agreement with available analytical solutions.