# An H-Adaptive solution of the Richards' Equation

**Abstract** --

The Richards’ equation describes mathematically the flow of water into the unsaturated soil zone. The model proposed here consists on applying adaptivity with *h-refinement* in finite element analysis and obtaining a numerical *h-adaptive* solution of classical Richards' equation. The Euler explicit method discretized the of term time derivative and to confirm the occurrence of the conservation of mass, this adaptive strategy was applied to different meshes with polynomial interpolation function of degree two. Moreover, the *h-refinement* and the interpolation ensure the concordance between the proposed model and available solutions. When compared with a numerical approximation obtained on uniform meshes, the simulation using *h-adaptive* scheme required a reduced computational effort.

**Keywords** --

Adapted mesh techniques, Numerical solution, *h-Refinement*,Unsaturated porous medium, Water flow.

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## About the Author

Maria de Lourdes P. Pizarro
Brazilian Air Force Academy, Estrada de Aguaí s/n 13.631-972, Pirassununga-SP, Brazil alessandroafj@afa.aer.mil.br
University of São Paulo, Av. Trabalhador Sancarlense, 400 ew@sc.usp.br |