In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the regular surfaces under consideration by triangular meshes, the key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial...

This paper explores the utilization of adaptive triangular meshes representing gray-level images to accelerate basic image processing operations. In particular, two algorithms for thresholding and labeling gray-level images represented with adaptive triangular meshes are described and evaluated. Experimental results with real gray-level images show that it is possible to perform faster by worki...

Abstract. We give here an error estimate for a finite volume discretization of the Stokes equations in two space dimensions on equilateral triangular meshes. This work was initiated by an analogous result presented in [AA 02] for general triangular meshes. However, in this latter article, the result is not actually proven. We state here the restricting assumptions (namely equilateral triangles)...

Abstract. Lava flows present a significant natural hazard to communities around volcanoes and are typically slow-moving (<1 5 cm s−1) laminar. Recent lava during the 2018 eruption of Kīlauea volcano, Hawai'i, however, reached speeds as high 11 m s−1 were transitional turbulent. The formed complex network braided channels departing from classic rectangular channel geometry often employed by f...

In this paper we shall introduce a simple, effective numerical method to compute differential operators for scalar and vector-valued functions on regular surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly partial derivatives of functions defined on triangular meshes which are the discretizations of regular surfaces under consideration. Most im...

The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with conventional continuous Galerkin methods. However, allowing d...

In many parts of the world, snowmelt energetics are dominated by solar irradiance. This is particularly the case in the Canadian Rocky Mountains, where clear skies dominate the winter and spring. In mountains, solar irradiance at the snow surface is not only affected by solar angles, atmospheric transmittance, and the slope and aspect of immediate topography but also by shadows from surrounding...

Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured tria...