Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
A Particle-Partition of Unity Method--Part III: A Multilevel Solver
SIAM Journal on Scientific Computing
A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
SIAM Journal on Scientific Computing
A conforming finite element method for overlapping and nonmatching grids
Mathematics of Computation
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
A note on the conditioning of a class of generalized finite element methods
Applied Numerical Mathematics
Local-global multiscale model reduction for flows in high-contrast heterogeneous media
Journal of Computational Physics
Overlapping solution finite element method - Higher order approximation and implementation
Applied Numerical Mathematics
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We introduce a method for approximating essential boundary conditions-conditions of Dirichlet type-within the generalized finite element method (GFEM) framework. Our results apply to general elliptic boundary value problems of the form -@?"i","j"="1^n(a^i^ju"x"""i)"x"""j+@?"i"="1^nb^iu"x"""i+cu=f in @W, u=0 on @?@W, where @W is a smooth bounded domain. As test-trial spaces, we consider sequences of GFEM spaces, {S"@m}"@m"="1, which are nonconforming (that is S"@m@?H"0^1(@W)). We assume that @?v@?"L"^"2"("@?"@W")=