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- W4309783585 abstract "Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective treatment of the different boundary conditions that arise naturally in a variational formulation. Our formulation is based on introducing the gradient of the solution as an explicit variable, constrained using a Lagrange multiplier. The essential boundary conditions are enforced weakly, using Nitsche's method where required. As a result, the problem is rewritten as a saddle-point system, requiring analysis of the resulting finite-element discretization and the construction of optimal linear solvers. Here, we discuss the analysis of the well-posedness and accuracy of the finite-element formulation. Moreover, we develop monolithic multigrid solvers for the resulting linear systems. Two and three-dimensional numerical results are presented to demonstrate the accuracy of the discretization and efficiency of the multigrid solvers proposed." @default.
- W4309783585 created "2022-11-29" @default.
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- W4309783585 date "2022-12-01" @default.
- W4309783585 modified "2023-10-14" @default.
- W4309783585 title "A new mixed finite-element method for H2 elliptic problems" @default.
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- W4309783585 doi "https://doi.org/10.1016/j.camwa.2022.10.024" @default.
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