Liwei Shi

TL;DR: In this paper, an efficient nontraditional finite element method with nonbody-fitting grids is proposed to solve elasticity equations with sharp-edged interfaces in three dimensions, where the test function basis is the standard finite element basis independent of the interface and the solution basis is piecewise linear satisfying the jump conditions across the interface.

TL;DR: Numerical experiments demonstrate that the Petrov-Galerkin finite element interface method is nearly second order accurate in the L ∞ norm for interface problems, and it is accurate and efficient for computing the band structure of phononic crystals.

TL;DR: A non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged grids with Dirichlet and Neumann boundary conditions is proposed.

TL;DR: This paper presents an efficient non-traditional finite element method with non-body-fitting grids for three-dimensional elliptic interface problems with multi-domains and achieves close to second order accurate in the L∞ norm for piecewise smooth solutions.

TL;DR: An efficient non-traditional finite element method with non-body-fitted grids is proposed to solve elliptic interface problems and is approximately second order accurate in the L norm and L2 norm for piecewise smooth solutions.