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This study brings an adaptive mesh strategy applied to the numerical simulation of free-surface shallow water problems. In the solver the shallow water equations are integrated with the explicit two-step Taylor-Galerkin method. Equations are first discretized in time with a Taylor's series expansion and then in space using the Garlerkin technique. The finite element method with triangular unstructured meshes is used to solve the problem. An adaptive mesh strategy is added to the solver in order to obtain more precise solutions at low computational costs. The strategy consists in a mesh refinement and smoothing procedure that uses an error indicator and an adaptation criterion for the identification of the mesh elements that will be refined. The elements identified to be refined are divided in four new elements. Refinement closure is also performed to guarantee the integrity of the new mesh. In order to ensure a smooth transition among elements of different size, a smoothing procedure is applied to the mesh after its refinement. The elements to be refined are identified by error indicators that take into account the depth and velocity gradients. The adaptation criterion is defined based on these error indicators. The dam-break problem is solved with the proposed methodology and results are compared with previous published studies.

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