The TRUNC element in any dimension and application to a modified Poisson equation
<|reference_start|>The TRUNC element in any dimension and application to a modified Poisson equation: We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions.<|reference_end|>
@article{li2024the,
    title={The TRUNC element in any dimension and application to a modified Poisson
  equation},
    author={Hongliang Li, Pingbing Ming, Yinghong Zhou},
    journal={arXiv preprint arXiv:2409.00748},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00748},
    primaryClass={math.NA cs.NA}
}