--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Burgers1D.m	Mon Sep 03 14:50:27 2018 +0200
@@ -0,0 +1,97 @@
+classdef Burgers1D < scheme.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        h % Grid spacing
+        x % Grid
+        order % Order accuracy for the approximation
+
+        D % Non-stabalized scheme operator
+        M % Derivative norm
+        H % Discrete norm
+        Hi % Norm inverse
+        e_l
+        e_r
+        d_l
+        d_r
+        params % Parameters for the coefficient matrices
+    end
+
+    methods
+        function obj = Burgers1D(m, order, xlim, params)
+            [x, h] = util.get_grid(xlim{:},m);
+            ops = sbp.D2Variable(m, xlim, order);
+
+            obj.m = m;
+            obj.h = h;
+            obj.order = order;
+            obj.x = x;
+
+            D1 = ops.D1;
+            obj.D = @(v)(-1/3*v.*D1*v - 1/3*D1*v.^2 + ops.D2(params.eps)*v);
+            obj.M = ops.M;
+            obj.H =  ops.H;
+            obj.Hi = ops.HI;
+            obj.e_l = ops.e_l;
+            obj.e_r = ops.e_r;
+            obj.d_l =  ops.d1_l;
+            obj.d_r =  ops.d1_r;
+            obj.params = params;
+        end
+
+        % Closure functions return the opertors applied to the own doamin to close the boundary
+        % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other domain.
+        %       boundary            is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
+        %       type                is a string specifying the type of boundary condition if there are several.
+        %       data                is a function returning the data that should be applied at the boundary.
+        %       neighbour_scheme    is an instance of Scheme that should be interfaced to.
+        %       neighbour_boundary  is a string specifying which boundary to interface to.
+        function [closure, penalty] = boundary_condition(obj,boundary,type,data)
+            default_arg('type','robin');
+            default_arg('data',0);
+            [e, s, d] = obj.get_boundary_ops(boundary);
+            switch type
+                % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
+                case {'R','robin'}
+                    p = s*obj.Hi*e;
+                    closure = @(v) p*(e'*((v-s*abs(v))/3)*(e'*v) - e'*obj.params.eps*d'*v);
+                    switch class(data)
+                        case 'double'
+                            penalty = s*p*data;
+                        case 'function_handle'
+                            penalty = @(t) s*p*data(t);
+                        otherwise
+                            error('Wierd data argument!')
+                    end
+                % Unknown, boundary condition
+                otherwise
+                    error('No such boundary condition: type = %s',type);
+            end
+        end
+
+        % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
+        % The right boundary is considered the positive boundary
+        function [e, s, d] = get_boundary_ops(obj,boundary)
+            switch boundary
+                case 'l'
+                    e = obj.e_l;
+                    s = -1;
+                    d = obj.d_l;
+                case 'r'
+                    e = obj.e_r;
+                    s = 1;
+                    d = obj.d_r;
+                otherwise
+                    error('No such boundary: boundary = %s',boundary);
+            end
+        end
+
+        function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
+            error('An interface function does not exist yet');
+        end
+
+        function N = size(obj)
+            N = obj.m;
+        end
+
+    end
+end
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