Geodesic
Higher-order finite element methods for elliptic problems with interfaces
Guzmán, Johnny1 ; Sánchez, Manuel A.1 ; Sarkis, Marcus2
1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1561-1583

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We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.

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DOI : 10.1051/m2an/2015093
Classification : 65N30, 65N15
Keywords: Interface problems, finite elements, pointwise estimates

Guzmán, Johnny 1 ; Sánchez, Manuel A. 1 ; Sarkis, Marcus 2

1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA 
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     title = {Higher-order finite element methods for elliptic problems with interfaces},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1561--1583},
     publisher = {EDP-Sciences},
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Guzmán, Johnny; Sánchez, Manuel A.; Sarkis, Marcus. Higher-order finite element methods for elliptic problems with interfaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1561-1583. doi: 10.1051/m2an/2015093

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