Alexandre B. Simas

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math.NA2026

Mass Lumping and Numerical Quadrature for Approximation of Fractional Elliptic Differential Equations Driven by Gaussian White Noise

Kelvin J. R. Almeida-Sousa, David Bolin, Alexandre B. Simas

Fractional elliptic stochastic partial differential equations (SPDEs) are widely used in statistics and machine learning for computationally efficient and flexible modeling of Gaus…

math.NA2026

Numerical approximation of fractional diffusion equations on metric graphs

David Bolin, Lenin Riera-Segura, Alexandre B. Simas

We study fractional diffusion equations on compact metric graphs, where the nonlocal dynamics is governed by fractional powers of the shifted Kirchhoff-Laplacian. Building on recen…

math.NA2026

Finite element and box-method discretizations for fractional elliptic problems with quadrature and mass lumping

Kelvin J. R. Almeida-Sousa, David Bolin, Alexandre B. Simas

We analyze numerical approximation of the fractional elliptic problem $L^{β} u = f$ , $β > 0$ , where $L$ is a second-order self-adjoint elliptic operator with homogeneous Dirichlet or Ne…