Geodesic
Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1082-1092

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Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov–Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness. 
@article{ZVMMF_2016_56_6_a12,
     author = {N. G. Burago and I. S. Nikitin and V. L. Yakushev},
     title = {Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1082--1092},
     publisher = {mathdoc},
     volume = {56},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a12/}
}
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N. G. Burago; I. S. Nikitin; V. L. Yakushev. Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1082-1092. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a12/