Comparative Study of Weak Galerkin and Discontinuous Galerkin Finite Element Methods
Issue:
Volume 7, Issue 2, June 2022
Pages:
23-38
Received:
24 December 2021
Accepted:
23 April 2022
Published:
31 May 2022
DOI:
10.11648/j.ijssam.20220702.11
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Abstract: FEM is a valuable approximation tool for the solution of Partial Differential Equations when the analytical solutions are difficult or impossible to obtain due to complicated geometry or boundary conditions. The Project work involved collecting facts related to WG and DG‑FEMs. WG‑FEM is a numerical method that was first proposed and analyzed by Wang and Ye (2013) for general second‑order elliptic BVPs on triangular and rectangular meshes. DG‑FEMs as developed by Cockburn et al. (1970) uses a discontinuous function space to approximate the exact solution of the equations. The comparison and numerical examples demonstrated that WG‑FEMs are viable and hold some advantages over DG‑FEMs, due to their properties. Numerical examples demonstrated that WGM generates a smaller linear system to solve than the DGMs. WG‑FEM have less unknowns, no need for choosing penalty factor and normal flux is continuous across element interfaces compared to DG‑FEMs and the implementation of WG‑FEMs is easier than that of DG‑FEMs based on error and convergence rate. The computations were done by hand and with the help of MATLAB 2021Rb.
Abstract: FEM is a valuable approximation tool for the solution of Partial Differential Equations when the analytical solutions are difficult or impossible to obtain due to complicated geometry or boundary conditions. The Project work involved collecting facts related to WG and DG‑FEMs. WG‑FEM is a numerical method that was first proposed and analyzed by Wan...
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Markovian Approach for Analyzing Patient Flow Data: A Study of Kapsabet County Referral Hospital, Kenya
Merary Kipkogei,
Edgar Ouko Otumba
Issue:
Volume 7, Issue 2, June 2022
Pages:
39-45
Received:
10 June 2022
Accepted:
30 June 2022
Published:
12 July 2022
DOI:
10.11648/j.ijssam.20220702.12
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Abstract: Hospital is indispensable and necessary welfare of society. Through it, we can manage our illnesses by treatment and prevention interventions. With the rise incidences of chronic diseases and illnesses, there has been an increased demand for health care services round the world. This demand has subsequently caused a serious pressure resulting to serious episodes of congestion and overcrowding in hospitals. Hospital overcrowding and congestion, has always been a problem to patients, hospital administration and to the general health workers. Hospitals are struggling to alleviate congestion and overcrowding. In this study, we developed an objective patient flow estimation using Markov chain models. Weekly data from Kapsabet County Referral Hospital facility was used to assess the flow. Markov chains’ transition probability matrices were constructed for each day in a week. Markov chain’s four-state model used was; High, Medium, Low and Very Low. The future n step transition probabilities matrices were computed, giving rise to steady state for each day of the week. It was examined that the patient flow had some pattern through the Markov chains’ steady states. The steady state probability of the flow is high on Mondays with highest probability of 0.57. Medium on Tuesdays through to Thursdays with steady state probabilities ranging from 0.36 and 0.3 respectively. On Fridays the probabilities decrease from 0.22 to 0.12 on Sunday. Through this study, we can witness some pattern from steady state of transition matrices. This way, the patient’s population flow throughout the week at this facility is identified. Generally, through this study, the patient flow is understood and hence the patient flow congestion can be easily attenuated.
Abstract: Hospital is indispensable and necessary welfare of society. Through it, we can manage our illnesses by treatment and prevention interventions. With the rise incidences of chronic diseases and illnesses, there has been an increased demand for health care services round the world. This demand has subsequently caused a serious pressure resulting to se...
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