### Electronic Research Archive

2021, Issue 6: 4099-4118. doi: 10.3934/era.2021074
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# Some estimates of virtual element methods for fourth order problems

• Received: 01 November 2020 Revised: 01 July 2021 Published: 22 September 2021
• Primary: 65N30; Secondary: 35J40

• In this paper, we employ the techniques developed for second order operators to obtain the new estimates of Virtual Element Method for fourth order operators. The analysis bases on elements with proper shape regularity. Estimates for projection and interpolation operators are derived. Also, the biharmonic problem is solved by Virtual Element Method, optimal error estimates were obtained. Our choice of the discrete form for the right hand side function relaxes the regularity requirement in previous work and the error estimates between exact solutions and the computable numerical solutions were proved.

Citation: Qingguang Guan. Some estimates of virtual element methods for fourth order problems[J]. Electronic Research Archive, 2021, 29(6): 4099-4118. doi: 10.3934/era.2021074

### Related Papers:

• In this paper, we employ the techniques developed for second order operators to obtain the new estimates of Virtual Element Method for fourth order operators. The analysis bases on elements with proper shape regularity. Estimates for projection and interpolation operators are derived. Also, the biharmonic problem is solved by Virtual Element Method, optimal error estimates were obtained. Our choice of the discrete form for the right hand side function relaxes the regularity requirement in previous work and the error estimates between exact solutions and the computable numerical solutions were proved.

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