Characteristic Petrov-Galerkin subdomain methods for two-phase immiscible flow

DOI10.1016/0045-7825(87)90036-3zbMath0607.76103OpenAlexW2032885298MaRDI QIDQ1085748

Richard E. Ewing, Magne S. Espedal

Publication date: 1987

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(87)90036-3

zbMATH Keywords

diffusionnonlinear parabolic equationmixed finite element methodspreconditionershockscharacteristicssubstructuringtime-steppingshock solutionlocal a priori error estimateoptimal order of approximationPetrov- Galerkin finite element methodspure convection problemsaturation of water

Mathematics Subject Classification ID

Diffusion (76R50) Shock waves and blast waves in fluid mechanics (76L05) Multiphase and multicomponent flows (76T99) Basic methods in fluid mechanics (76M99)

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Cites Work

• Unnamed Item
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• Discontinuous upwinding and mixed finite elements for two-phase flows in reservoir simulation
• Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
• Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
• An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables
• A preconditioning technique for the efficient solution of problems with local grid refinement
• Perturbation methods in applied mathematics
• The approximation of the pressure by a mixed method in the simulation of miscible displacement
• The Scalar Riemann Problem in Two Spatial Dimensions: Piecewise Smoothness of Solutions and Its Breakdown
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Efficient Time-Stepping Methods for Miscible Displacement Problems in Porous Media
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation