Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids
Journal of Computational Physics
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
SIAM Journal on Numerical Analysis
Discontinuous enrichment methods for computational fluid dynamics
Discontinuous enrichment methods for computational fluid dynamics
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We discuss the numerical integration of polynomials times non-polynomial weighting functions in two dimensions arising from multiscale finite element computations. The proposed quadrature rules are significantly more accurate than standard quadratures and are better suited to existing finite element codes than formulas computed by symbolic integration. We validate this approach by introducing the new quadrature formulas into a multiscale finite element method for the two-dimensional reaction-diffusion equation.