1. C0-hybrid high-order methods for biharmonic problems.
- Author
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Dong, Zhaonan and Ern, Alexandre
- Abstract
We devise and analyze |$C^0$| -conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. |$C^0$| -conforming HHO methods hinge on cell unknowns that are |$C^0$| -conforming polynomials of order |$(k+2)$| approximating the solution in the mesh cells and on face unknowns, which are polynomials of order |$k\ge 0$| approximating the normal derivative of the solution on the mesh skeleton. Such methods deliver |$O(h^{k+1})$| |$H^2$| -error estimates for smooth solutions. An important novelty in the error analysis is to lower the minimal regularity requirement on the exact solution. The technique to achieve this has a broader applicability than just |$C^0$| -conforming HHO methods, and to illustrate this point, we outline the error analysis for the well-known |$C^0$| -conforming interior penalty discontinuous Galerkin methods as well. The present technique does not require a |$C^1$| -smoother to evaluate the right-hand side in case of rough loads; loads in |$W^{-1,q}$| , |$q>\frac {2d}{d+2}$| , are covered, but not in |$H^{-2}$|. Finally, numerical results including comparisons to various existing methods showcase the efficiency of the proposed |$C^0$| -conforming HHO methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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