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This paper is concerned with the initial-boundary value problems of scalar transport equations with uncertain transport velocities. It was demonstrated in our earlier works that regularity of the exact solutions in the random spaces (or the parametric spac ...
The level set method is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issue ...
Institute of Electrical and Electronics Engineers2012
This project deals with the finite element approximation of an inverse problem for the monodomain equation, which models the propagation of the electrical potential in the cardiac muscle. The goal consists in recovering the shape of an infarcted area inside ...
Discontinuous Galerkin (DG) methods for the numerical solution of par- tial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy withou ...
We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyp ...
A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...
This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...
The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L^2 and the H^1 ...
We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...
An explicit scheme for wave propagation modeling of indoor environments is presented. The technique is based on the hybrid parabolic-integral equation method, which provides a correction to the parabolic equation method through a Green's function formulati ...
